LMFDB - Embedded newform 76.2.k.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	76.3
Dual form			76.2.k.a.51.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35051 + 0.419681i) q^{2} +(-1.23656 + 0.450071i) q^{3} +(1.64774 - 1.13356i) q^{4} +(-0.503046 + 2.85292i) q^{5} +(1.48110 - 1.12678i) q^{6} +(-2.71118 + 1.56530i) q^{7} +(-1.74954 + 2.22241i) q^{8} +(-0.971618 + 0.815285i) q^{9} +O(q^{10})$	\(q+(-1.35051 + 0.419681i) q^{2} +(-1.23656 + 0.450071i) q^{3} +(1.64774 - 1.13356i) q^{4} +(-0.503046 + 2.85292i) q^{5} +(1.48110 - 1.12678i) q^{6} +(-2.71118 + 1.56530i) q^{7} +(-1.74954 + 2.22241i) q^{8} +(-0.971618 + 0.815285i) q^{9} +(-0.517948 - 4.06400i) q^{10} +(3.30359 + 1.90733i) q^{11} +(-1.52734 + 2.14332i) q^{12} +(1.53341 - 4.21300i) q^{13} +(3.00454 - 3.25178i) q^{14} +(-0.661968 - 3.75421i) q^{15} +(1.43006 - 3.73563i) q^{16} +(0.0599755 + 0.0503255i) q^{17} +(0.970017 - 1.50882i) q^{18} +(3.51689 + 2.57517i) q^{19} +(2.40508 + 5.27109i) q^{20} +(2.64804 - 3.15581i) q^{21} +(-5.26199 - 1.18940i) q^{22} +(-2.21189 + 0.390015i) q^{23} +(1.16317 - 3.53556i) q^{24} +(-3.18761 - 1.16020i) q^{25} +(-0.302759 + 6.33322i) q^{26} +(2.80841 - 4.86430i) q^{27} +(-2.69294 + 5.65251i) q^{28} +(0.332156 + 0.395848i) q^{29} +(2.46956 + 4.79226i) q^{30} +(-1.35392 - 2.34507i) q^{31} +(-0.363540 + 5.64516i) q^{32} +(-4.94351 - 0.871675i) q^{33} +(-0.102118 - 0.0427943i) q^{34} +(-3.10183 - 8.52220i) q^{35} +(-0.676793 + 2.44476i) q^{36} +10.4844i q^{37} +(-5.83033 - 2.00181i) q^{38} +5.89976i q^{39} +(-5.46025 - 6.10927i) q^{40} +(0.203213 + 0.558324i) q^{41} +(-2.25176 + 5.37328i) q^{42} +(10.9034 + 1.92257i) q^{43} +(7.60552 - 0.602057i) q^{44} +(-1.83717 - 3.18207i) q^{45} +(2.82348 - 1.45500i) q^{46} +(1.45618 + 1.73541i) q^{47} +(-0.0870632 + 5.26296i) q^{48} +(1.40035 - 2.42547i) q^{49} +(4.79180 + 0.229071i) q^{50} +(-0.0968133 - 0.0352372i) q^{51} +(-2.24906 - 8.68012i) q^{52} +(0.929735 - 0.163937i) q^{53} +(-1.75132 + 7.74791i) q^{54} +(-7.10330 + 8.46538i) q^{55} +(1.26459 - 8.76392i) q^{56} +(-5.50785 - 1.60150i) q^{57} +(-0.614709 - 0.395196i) q^{58} +(-6.93627 - 5.82022i) q^{59} +(-5.34638 - 5.43556i) q^{60} +(-0.585413 - 3.32004i) q^{61} +(2.81266 + 2.59881i) q^{62} +(1.35807 - 3.73126i) q^{63} +(-1.87820 - 7.77640i) q^{64} +(11.2480 + 6.49401i) q^{65} +(7.04207 - 0.897497i) q^{66} +(-1.61972 + 1.35911i) q^{67} +(0.155871 + 0.0149369i) q^{68} +(2.55959 - 1.47778i) q^{69} +(7.76564 + 10.2075i) q^{70} +(-0.503163 + 2.85358i) q^{71} +(-0.112009 - 3.58571i) q^{72} +(13.7341 - 4.99880i) q^{73} +(-4.40011 - 14.1593i) q^{74} +4.46384 q^{75} +(8.71402 + 0.256572i) q^{76} -11.9422 q^{77} +(-2.47602 - 7.96767i) q^{78} +(-6.53766 + 2.37952i) q^{79} +(9.93804 + 5.95905i) q^{80} +(-0.622736 + 3.53171i) q^{81} +(-0.508759 - 0.668736i) q^{82} +(4.69715 - 2.71190i) q^{83} +(0.785956 - 8.20167i) q^{84} +(-0.173745 + 0.145789i) q^{85} +(-15.5320 + 1.97952i) q^{86} +(-0.588891 - 0.339996i) q^{87} +(-10.0186 + 4.00497i) q^{88} +(1.01763 - 2.79592i) q^{89} +(3.81656 + 3.52638i) q^{90} +(2.43727 + 13.8225i) q^{91} +(-3.20249 + 3.14996i) q^{92} +(2.72965 + 2.29045i) q^{93} +(-2.69489 - 1.73255i) q^{94} +(-9.11589 + 8.73797i) q^{95} +(-2.09118 - 7.14419i) q^{96} +(-6.08391 + 7.25052i) q^{97} +(-0.873252 + 3.86331i) q^{98} +(-4.76484 + 0.840170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.35051	+	0.419681i	−0.954952	+	0.296759i
$2$	−1.35051	+	0.419681i	−0.954952	+	0.296759i
$3$	−1.23656	+	0.450071i	−0.713928	+	0.259848i	−0.673346	−	0.739328i	$-0.735143\pi$
$3$	−1.23656	+	0.450071i	−0.713928	+	0.259848i	−0.0405821	+	0.999176i	$0.512921\pi$
$4$	1.64774	−	1.13356i	0.823868	−	0.566782i
$5$	−0.503046	+	2.85292i	−0.224969	+	1.27586i	0.637775	+	0.770222i	$0.279855\pi$
$5$	−0.503046	+	2.85292i	−0.224969	+	1.27586i	−0.862744	+	0.505640i	$0.831256\pi$
$6$	1.48110	−	1.12678i	0.604655	−	0.460008i
$7$	−2.71118	+	1.56530i	−1.02473	+	0.591629i	−0.915471	−	0.402384i	$-0.868182\pi$
$7$	−2.71118	+	1.56530i	−1.02473	+	0.591629i	−0.109260	+	0.994013i	$0.534848\pi$
$8$	−1.74954	+	2.22241i	−0.618557	+	0.785740i
$9$	−0.971618	+	0.815285i	−0.323873	+	0.271762i
$10$	−0.517948	−	4.06400i	−0.163790	−	1.28515i
$11$	3.30359	+	1.90733i	0.996069	+	0.575081i	0.907083	−	0.420952i	$-0.138304\pi$
$11$	3.30359	+	1.90733i	0.996069	+	0.575081i	0.0889863	+	0.996033i	$0.471637\pi$
$12$	−1.52734	+	2.14332i	−0.440905	+	0.618722i
$13$	1.53341	−	4.21300i	0.425290	−	1.16848i	−0.523350	−	0.852118i	$-0.675318\pi$
$13$	1.53341	−	4.21300i	0.425290	−	1.16848i	0.948640	−	0.316358i	$-0.102460\pi$
$14$	3.00454	−	3.25178i	0.802998	−	0.869076i
$15$	−0.661968	−	3.75421i	−0.170919	−	0.969332i
$16$	1.43006	−	3.73563i	0.357516	−	0.933907i
$17$	0.0599755	+	0.0503255i	0.0145462	+	0.0122057i	0.650032	−	0.759907i	$-0.274756\pi$
$17$	0.0599755	+	0.0503255i	0.0145462	+	0.0122057i	−0.635486	+	0.772113i	$0.719200\pi$
$18$	0.970017	−	1.50882i	0.228635	−	0.355632i
$19$	3.51689	+	2.57517i	0.806830	+	0.590784i
$19$	3.51689	+	2.57517i	0.806830	+	0.590784i
$20$	2.40508	+	5.27109i	0.537791	+	1.17865i
$21$	2.64804	−	3.15581i	0.577850	−	0.688655i
$22$	−5.26199	−	1.18940i	−1.12186	−	0.253582i
$23$	−2.21189	+	0.390015i	−0.461210	+	0.0813238i	−0.399425	−	0.916766i	$-0.630790\pi$
$23$	−2.21189	+	0.390015i	−0.461210	+	0.0813238i	−0.0617846	+	0.998090i	$0.519679\pi$
$24$	1.16317	−	3.53556i	0.237431	−	0.721693i
$25$	−3.18761	−	1.16020i	−0.637522	−	0.232039i
$26$	−0.302759	+	6.33322i	−0.0593759	+	1.24205i
$27$	2.80841	−	4.86430i	0.540478	−	0.936135i
$28$	−2.69294	+	5.65251i	−0.508918	+	1.06822i
$29$	0.332156	+	0.395848i	0.0616799	+	0.0735072i	0.796002	−	0.605294i	$-0.206944\pi$
$29$	0.332156	+	0.395848i	0.0616799	+	0.0735072i	−0.734322	+	0.678801i	$0.762500\pi$
$30$	2.46956	+	4.79226i	0.450878	+	0.874944i
$31$	−1.35392	−	2.34507i	−0.243172	−	0.421186i	0.718444	−	0.695585i	$-0.244855\pi$
$31$	−1.35392	−	2.34507i	−0.243172	−	0.421186i	−0.961616	+	0.274398i	$0.911521\pi$
$32$	−0.363540	+	5.64516i	−0.0642653	+	0.997933i
$33$	−4.94351	−	0.871675i	−0.860555	−	0.151739i
$34$	−0.102118	−	0.0427943i	−0.0175131	−	0.00733915i
$35$	−3.10183	−	8.52220i	−0.524304	−	1.44051i
$36$	−0.676793	+	2.44476i	−0.112799	+	0.407461i
$37$			10.4844i			1.72363i	0.507227	+	0.861813i	$0.330671\pi$
$37$			10.4844i			1.72363i	−0.507227	+	0.861813i	$0.669329\pi$
$38$	−5.83033	−	2.00181i	−0.945805	−	0.324736i
$39$			5.89976i			0.944718i
$40$	−5.46025	−	6.10927i	−0.863341	−	0.965961i
$41$	0.203213	+	0.558324i	0.0317366	+	0.0871956i	0.954549	−	0.298054i	$-0.0963376\pi$
$41$	0.203213	+	0.558324i	0.0317366	+	0.0871956i	−0.922812	+	0.385250i	$0.874115\pi$
$42$	−2.25176	+	5.37328i	−0.347455	+	0.829115i
$43$	10.9034	+	1.92257i	1.66276	+	0.293189i	0.924457	−	0.381286i	$-0.124519\pi$
$43$	10.9034	+	1.92257i	1.66276	+	0.293189i	0.738298	+	0.674474i	$0.235630\pi$
$44$	7.60552	−	0.602057i	1.14657	−	0.0907636i
$45$	−1.83717	−	3.18207i	−0.273869	−	0.474355i
$46$	2.82348	−	1.45500i	0.416300	−	0.214529i
$47$	1.45618	+	1.73541i	0.212405	+	0.253135i	0.861719	−	0.507386i	$-0.169388\pi$
$47$	1.45618	+	1.73541i	0.212405	+	0.253135i	−0.649314	+	0.760521i	$0.724944\pi$
$48$	−0.0870632	+	5.26296i	−0.0125665	+	0.759642i
$49$	1.40035	−	2.42547i	0.200049	−	0.346496i
$50$	4.79180	+	0.229071i	0.677663	+	0.0323956i
$51$	−0.0968133	−	0.0352372i	−0.0135566	−	0.00493419i
$52$	−2.24906	−	8.68012i	−0.311888	−	1.20372i
$53$	0.929735	−	0.163937i	0.127709	−	0.0225185i	−0.109428	−	0.993995i	$-0.534902\pi$
$53$	0.929735	−	0.163937i	0.127709	−	0.0225185i	0.237137	+	0.971476i	$0.423791\pi$
$54$	−1.75132	+	7.74791i	−0.238324	+	1.05436i
$55$	−7.10330	+	8.46538i	−0.957809	+	1.14147i
$56$	1.26459	−	8.76392i	0.168988	−	1.17113i
$57$	−5.50785	−	1.60150i	−0.729533	−	0.212123i
$58$	−0.614709	−	0.395196i	−0.0807153	−	0.0518918i
$59$	−6.93627	−	5.82022i	−0.903025	−	0.757728i	0.0677542	−	0.997702i	$-0.478417\pi$
$59$	−6.93627	−	5.82022i	−0.903025	−	0.757728i	−0.970779	+	0.239974i	$0.922861\pi$
$60$	−5.34638	−	5.43556i	−0.690215	−	0.701727i
$61$	−0.585413	−	3.32004i	−0.0749544	−	0.425088i	−0.999076	−	0.0429882i	$-0.986312\pi$
$61$	−0.585413	−	3.32004i	−0.0749544	−	0.425088i	0.924121	−	0.382100i	$-0.124799\pi$
$62$	2.81266	+	2.59881i	0.357209	+	0.330049i
$63$	1.35807	−	3.73126i	0.171101	−	0.470095i
$64$	−1.87820	−	7.77640i	−0.234776	−	0.972050i
$65$	11.2480	+	6.49401i	1.39514	+	0.805483i
$66$	7.04207	−	0.897497i	0.866819	−	0.110474i
$67$	−1.61972	+	1.35911i	−0.197881	+	0.166042i	−0.736344	−	0.676607i	$-0.763450\pi$
$67$	−1.61972	+	1.35911i	−0.197881	+	0.166042i	0.538463	+	0.842649i	$0.319005\pi$
$68$	0.155871	+	0.0149369i	0.0189021	+	0.00181137i
$69$	2.55959	−	1.47778i	0.308139	−	0.177904i
$70$	7.76564	+	10.2075i	0.928172	+	1.22003i
$71$	−0.503163	+	2.85358i	−0.0597145	+	0.338657i	−0.999998	−	0.00173334i	$-0.999448\pi$
$71$	−0.503163	+	2.85358i	−0.0597145	+	0.338657i	0.940284	+	0.340391i	$0.110559\pi$
$72$	−0.112009	−	3.58571i	−0.0132003	−	0.422580i
$73$	13.7341	−	4.99880i	1.60745	−	0.585066i	0.626520	−	0.779405i	$-0.284479\pi$
$73$	13.7341	−	4.99880i	1.60745	−	0.585066i	0.980934	+	0.194340i	$0.0622563\pi$
$74$	−4.40011	−	14.1593i	−0.511502	−	1.64598i
$75$	4.46384			0.515440
$76$	8.71402	+	0.256572i	0.999567	+	0.0294308i
$77$	−11.9422			−1.36094
$78$	−2.47602	−	7.96767i	−0.280354	−	0.902161i
$79$	−6.53766	+	2.37952i	−0.735545	+	0.267716i	−0.682510	−	0.730876i	$-0.739112\pi$
$79$	−6.53766	+	2.37952i	−0.735545	+	0.267716i	−0.0530348	+	0.998593i	$0.516889\pi$
$80$	9.93804	+	5.95905i	1.11111	+	0.666242i
$81$	−0.622736	+	3.53171i	−0.0691929	+	0.392413i
$82$	−0.508759	−	0.668736i	−0.0561831	−	0.0738495i
$83$	4.69715	−	2.71190i	0.515579	−	0.297670i	−0.219545	−	0.975602i	$-0.570457\pi$
$83$	4.69715	−	2.71190i	0.515579	−	0.297670i	0.735124	+	0.677933i	$0.237124\pi$
$84$	0.785956	−	8.20167i	0.0857548	−	0.894876i
$85$	−0.173745	+	0.145789i	−0.0188453	+	0.0158131i
$86$	−15.5320	+	1.97952i	−1.67486	+	0.213457i
$87$	−0.588891	−	0.339996i	−0.0631357	−	0.0364514i
$88$	−10.0186	+	4.00497i	−1.06799	+	0.426932i
$89$	1.01763	−	2.79592i	0.107869	−	0.296367i	−0.874001	−	0.485924i	$-0.838483\pi$
$89$	1.01763	−	2.79592i	0.107869	−	0.296367i	0.981870	+	0.189557i	$0.0607053\pi$
$90$	3.81656	+	3.52638i	0.402301	+	0.371713i
$91$	2.43727	+	13.8225i	0.255496	+	1.44899i
$92$	−3.20249	+	3.14996i	−0.333883	+	0.328406i
$93$	2.72965	+	2.29045i	0.283052	+	0.237509i
$94$	−2.69489	−	1.73255i	−0.277957	−	0.178698i
$95$	−9.11589	+	8.73797i	−0.935271	+	0.896496i
$96$	−2.09118	−	7.14419i	−0.213431	−	0.729151i
$97$	−6.08391	+	7.25052i	−0.617728	+	0.736179i	−0.980678	−	0.195629i	$-0.937325\pi$
$97$	−6.08391	+	7.25052i	−0.617728	+	0.736179i	0.362950	+	0.931808i	$0.381769\pi$
$98$	−0.873252	+	3.86331i	−0.0882118	+	0.390253i
$99$	−4.76484	+	0.840170i	−0.478885	+	0.0844403i
$100$	−6.56750	+	1.70167i	−0.656750	+	0.170167i
$101$	−15.0894	−	5.49209i	−1.50145	−	0.546483i	−0.545014	−	0.838427i	$-0.683476\pi$
$101$	−15.0894	−	5.49209i	−1.50145	−	0.546483i	−0.956435	+	0.291944i	$0.905698\pi$
$102$	0.145535	+	0.00695730i	0.0144102	+	0.000688876i
$103$	5.69920	−	9.87131i	0.561559	−	0.972649i	−0.435802	−	0.900043i	$-0.643535\pi$
$103$	5.69920	−	9.87131i	0.561559	−	0.972649i	0.997361	−	0.0726061i	$-0.0231316\pi$
$104$	6.68025	+	10.7787i	0.655052	+	1.05694i
$105$	7.67119	+	9.14216i	0.748631	+	0.892184i
$106$	−1.18681	+	0.611591i	−0.115273	+	0.0594029i
$107$	4.47937	+	7.75849i	0.433037	+	0.750041i	0.997133	−	0.0756674i	$-0.0241087\pi$
$107$	4.47937	+	7.75849i	0.433037	+	0.750041i	−0.564096	+	0.825709i	$0.690775\pi$
$108$	−0.886488	−	11.1986i	−0.0853023	−	1.07758i
$109$	15.8051	+	2.78687i	1.51386	+	0.266934i	0.868015	−	0.496539i	$-0.165396\pi$
$109$	15.8051	+	2.78687i	1.51386	+	0.266934i	0.645841	+	0.763472i	$0.276507\pi$
$110$	6.04029	−	14.4137i	0.575919	−	1.37429i
$111$	−4.71872	−	12.9646i	−0.447881	−	1.23054i
$112$	1.97022	+	12.3665i	0.186168	+	1.16852i
$113$		−	7.86582i		−	0.739954i	−0.929041	−	0.369977i	$-0.879366\pi$
$113$		−	7.86582i		−	0.739954i	0.929041	−	0.369977i	$-0.120634\pi$
$114$	8.11051	−	0.148710i	0.759618	−	0.0139280i
$115$		−	6.50652i		−	0.606736i
$116$	0.996025	+	0.275733i	0.0924786	+	0.0256012i
$117$	1.94491	+	5.34359i	0.179807	+	0.494015i
$118$	11.8101	+	4.94922i	1.08721	+	0.455613i
$119$	−0.241379	−	0.0425617i	−0.0221272	−	0.00390162i
$120$	9.50152	+	5.09698i	0.867366	+	0.465288i
$121$	1.77579	+	3.07577i	0.161436	+	0.279615i
$122$	2.18396	+	4.23805i	0.197727	+	0.383695i
$123$	−0.502571	−	0.598941i	−0.0453153	−	0.0540047i
$124$	−4.88919	−	2.32929i	−0.439062	−	0.209176i
$125$	−2.32886	+	4.03371i	−0.208300	+	0.360786i
$126$	−0.268140	+	5.60905i	−0.0238878	+	0.499694i
$127$	−13.7632	−	5.00938i	−1.22128	−	0.444511i	−0.350679	−	0.936496i	$-0.614049\pi$
$127$	−13.7632	−	5.00938i	−1.22128	−	0.444511i	−0.870604	+	0.491985i	$0.836271\pi$
$128$	5.80013	+	9.71383i	0.512664	+	0.858589i
$129$	−14.3480	+	2.52994i	−1.26327	+	0.222749i
$130$	−17.9159	−	4.04965i	−1.57132	−	0.355178i
$131$	12.0116	−	14.3149i	1.04946	−	1.25070i	0.0822765	−	0.996610i	$-0.473781\pi$
$131$	12.0116	−	14.3149i	1.04946	−	1.25070i	0.967182	−	0.254086i	$-0.0817746\pi$
$132$	−9.13370	+	4.16750i	−0.794987	+	0.362734i
$133$	−13.5659	−	1.47675i	−1.17631	−	0.128050i
$134$	1.61706	−	2.51525i	0.139692	−	0.217285i
$135$	12.4647	+	10.4591i	1.07279	+	0.900177i
$136$	−0.216774	+	0.0452437i	−0.0185882	+	0.00387961i
$137$	−2.78187	−	15.7768i	−0.237671	−	1.34790i	−0.836914	−	0.547334i	$-0.815643\pi$
$137$	−2.78187	−	15.7768i	−0.237671	−	1.34790i	0.599243	−	0.800568i	$-0.295469\pi$
$138$	−2.83655	+	3.06997i	−0.241463	+	0.261333i
$139$	−4.01315	+	11.0260i	−0.340391	+	0.935215i	0.644891	+	0.764275i	$0.276903\pi$
$139$	−4.01315	+	11.0260i	−0.340391	+	0.935215i	−0.985281	+	0.170941i	$0.945319\pi$
$140$	−14.7714	−	10.5262i	−1.24842	−	0.889627i
$141$	−2.58171	−	1.49055i	−0.217419	−	0.125527i
$142$	−0.518068	−	4.06494i	−0.0434753	−	0.341123i
$143$	13.1013	−	10.9933i	1.09559	−	0.919306i
$144$	1.65612	+	4.79551i	0.138010	+	0.399626i
$145$	−1.29641	+	0.748484i	−0.107661	+	0.0621582i
$146$	−16.4501	+	12.5149i	−1.36142	+	1.03574i
$147$	−0.639977	+	3.62949i	−0.0527844	+	0.299355i
$148$	11.8847	+	17.2755i	0.976920	+	1.42004i
$149$	14.4819	−	5.27097i	1.18640	−	0.431815i	0.327943	−	0.944697i	$-0.393645\pi$
$149$	14.4819	−	5.27097i	1.18640	−	0.431815i	0.858459	+	0.512882i	$0.171422\pi$
$150$	−6.02844	+	1.87339i	−0.492220	+	0.152962i
$151$	8.07351			0.657013			0.328506	−	0.944502i	$-0.393455\pi$
$151$	8.07351			0.657013			0.328506	+	0.944502i	$0.393455\pi$
$152$	−11.8760	+	3.31061i	−0.963272	+	0.268526i
$153$	−0.0993029			−0.00802816
$154$	16.1280	−	5.01191i	1.29963	−	0.403871i
$155$	7.37136	−	2.68296i	0.592082	−	0.215500i
$156$	6.68776	+	9.72125i	0.535449	+	0.778323i
$157$	0.547741	−	3.10639i	0.0437145	−	0.247917i	−0.955118	−	0.296226i	$-0.904272\pi$
$157$	0.547741	−	3.10639i	0.0437145	−	0.247917i	0.998832	+	0.0483086i	$0.0153831\pi$
$158$	7.83052	−	5.95729i	0.622963	−	0.473936i
$159$	−1.07589	+	0.621165i	−0.0853236	+	0.0492616i
$160$	−15.9223	−	3.87692i	−1.25877	−	0.306498i
$161$	5.38634	−	4.51967i	0.424503	−	0.356200i
$162$	−0.641184	−	5.03095i	−0.0503762	−	0.395269i
$163$	−7.85954	−	4.53771i	−0.615607	−	0.355421i	0.159550	−	0.987190i	$-0.448996\pi$
$163$	−7.85954	−	4.53771i	−0.615607	−	0.355421i	−0.775157	+	0.631769i	$0.782329\pi$
$164$	0.967738	+	0.689615i	0.0755677	+	0.0538499i
$165$	4.97363	−	13.6649i	0.387197	−	1.06381i
$166$	−5.20540	+	5.63374i	−0.404017	+	0.437263i
$167$	−2.01187	−	11.4099i	−0.155684	−	0.882925i	−0.958158	−	0.286239i	$-0.907595\pi$
$167$	−2.01187	−	11.4099i	−0.155684	−	0.882925i	0.802475	−	0.596686i	$-0.203516\pi$
$168$	2.38065	+	11.4063i	0.183671	+	0.880012i
$169$	−5.43945	−	4.56424i	−0.418419	−	0.351095i
$170$	0.173458	−	0.269807i	0.0133037	−	0.0206932i
$171$	−5.51657	+	0.365188i	−0.421863	+	0.0279266i
$172$	20.1453	−	9.19184i	1.53606	−	0.700871i
$173$	1.95957	−	2.33532i	0.148983	−	0.177551i	−0.686391	−	0.727232i	$-0.740806\pi$
$173$	1.95957	−	2.33532i	0.148983	−	0.177551i	0.835375	+	0.549681i	$0.185251\pi$
$174$	0.937990	+	0.212021i	0.0711089	+	0.0160733i
$175$	10.4583	−	1.84407i	0.790570	−	0.139399i
$176$	11.8494	−	9.61337i	0.893183	−	0.724635i
$177$	11.1966	+	4.07524i	0.841589	+	0.306313i
$178$	−0.200923	+	4.20299i	−0.0150598	+	0.315027i
$179$	−2.16782	+	3.75477i	−0.162030	+	0.280645i	−0.935597	−	0.353070i	$-0.885138\pi$
$179$	−2.16782	+	3.75477i	−0.162030	+	0.280645i	0.773566	+	0.633715i	$0.218471\pi$
$180$	−6.63425	−	3.16066i	−0.494488	−	0.235582i
$181$	1.29207	+	1.53983i	0.0960386	+	0.114454i	0.811923	−	0.583764i	$-0.198421\pi$
$181$	1.29207	+	1.53983i	0.0960386	+	0.114454i	−0.715885	+	0.698219i	$0.753976\pi$
$182$	−9.09258	−	17.6444i	−0.673987	−	1.30789i
$183$	2.21815	+	3.84195i	0.163970	+	0.284005i
$184$	3.00301	−	5.59806i	0.221385	−	0.412695i
$185$	−29.9111	−	5.27414i	−2.19911	−	0.387762i
$186$	−4.64767	−	1.94769i	−0.340784	−	0.142811i
$187$	0.102147	+	0.280648i	0.00746976	+	0.0205230i
$188$	4.36659	+	1.20882i	0.318466	+	0.0881621i
$189$			17.5840i			1.27905i
$190$	8.64391	−	15.6264i	0.627095	−	1.13366i
$191$			7.09667i			0.513497i	0.966478	+	0.256749i	$0.0826512\pi$
$191$			7.09667i			0.513497i	−0.966478	+	0.256749i	$0.917349\pi$
$192$	5.82244	+	8.77065i	0.420198	+	0.632967i
$193$	−1.24224	−	3.41304i	−0.0894186	−	0.245676i	0.886920	−	0.461923i	$-0.152840\pi$
$193$	−1.24224	−	3.41304i	−0.0894186	−	0.245676i	−0.976339	+	0.216247i	$0.930618\pi$
$194$	5.17345	−	12.3452i	0.371432	−	0.886332i
$195$	−16.8315	−	2.96785i	−1.20533	−	0.212532i
$196$	−0.442026	−	5.58391i	−0.0315733	−	0.398851i
$197$	8.46348	+	14.6592i	0.602998	+	1.04442i	0.992364	+	0.123340i	$0.0393607\pi$
$197$	8.46348	+	14.6592i	0.602998	+	1.04442i	−0.389366	+	0.921083i	$0.627306\pi$
$198$	6.08234	−	3.13437i	0.432253	−	0.222750i
$199$	4.24439	+	5.05827i	0.300877	+	0.358571i	0.895207	−	0.445650i	$-0.147027\pi$
$199$	4.24439	+	5.05827i	0.300877	+	0.358571i	−0.594331	+	0.804221i	$0.702583\pi$
$200$	8.15529	−	5.05436i	0.576666	−	0.357398i
$201$	1.39119	−	2.40961i	0.0981269	−	0.169961i
$202$	22.6832	+	1.08437i	1.59599	+	0.0762959i
$203$	−1.52016	−	0.553293i	−0.106694	−	0.0388335i
$204$	−0.199466	+	0.0516826i	−0.0139654	+	0.00361850i
$205$	−1.69508	+	0.298888i	−0.118389	+	0.0208752i
$206$	−3.55401	+	15.7231i	−0.247619	+	1.09548i
$207$	1.83113	−	2.18226i	0.127273	−	0.151678i
$208$	−13.5453	−	11.7531i	−0.939199	−	0.814931i
$209$	6.70667	+	15.2151i	0.463910	+	1.05245i
$210$	−14.1968	−	9.12710i	−0.979671	−	0.629830i
$211$	−1.14737	−	0.962755i	−0.0789880	−	0.0662788i	0.602439	−	0.798165i	$-0.294196\pi$
$211$	−1.14737	−	0.962755i	−0.0789880	−	0.0662788i	−0.681427	+	0.731886i	$0.738640\pi$
$212$	1.34612	−	1.32404i	0.0924522	−	0.0909354i
$213$	−0.662122	−	3.75508i	−0.0453678	−	0.257294i
$214$	−9.30550	−	8.59798i	−0.636111	−	0.587746i
$215$	−10.9698	+	30.1394i	−0.748137	+	2.05549i
$216$	5.89704	+	14.7517i	0.401243	+	1.00373i
$217$	7.34148	+	4.23860i	0.498372	+	0.287735i
$218$	−22.5145	+	2.86942i	−1.52487	+	0.194342i
$219$	−14.7332	+	12.3626i	−0.995578	+	0.835389i
$220$	−2.10831	+	22.0008i	−0.142142	+	1.48329i
$221$	0.303988	−	0.175508i	0.0204484	−	0.0118059i
$222$	11.8137	+	15.5284i	0.792881	+	1.04220i
$223$	1.36458	−	7.73892i	0.0913791	−	0.518237i	−0.904418	−	0.426648i	$-0.859694\pi$
$223$	1.36458	−	7.73892i	0.0913791	−	0.518237i	0.995797	−	0.0915888i	$-0.0291945\pi$
$224$	−7.85076	−	15.8741i	−0.524551	−	1.06063i
$225$	4.04303	−	1.47154i	0.269535	−	0.0981028i
$226$	3.30113	+	10.6228i	0.219588	+	0.706620i
$227$	−5.35801			−0.355624			−0.177812	−	0.984065i	$-0.556902\pi$
$227$	−5.35801			−0.355624			−0.177812	+	0.984065i	$0.556902\pi$
$228$	−10.8909	+	3.60466i	−0.721266	+	0.238724i
$229$	3.14192			0.207624			0.103812	−	0.994597i	$-0.466896\pi$
$229$	3.14192			0.207624			0.103812	+	0.994597i	$0.466896\pi$
$230$	2.73066	+	8.78709i	0.180055	+	0.579404i
$231$	14.7672	−	5.37483i	0.971611	−	0.353638i
$232$	−1.46086	+	0.0456336i	−0.0959100	+	0.00299599i
$233$	−2.48023	+	14.0661i	−0.162485	+	0.921500i	0.789134	+	0.614221i	$0.210530\pi$
$233$	−2.48023	+	14.0661i	−0.162485	+	0.921500i	−0.951619	+	0.307279i	$0.900582\pi$
$234$	−4.86921	−	6.40031i	−0.318310	−	0.418401i
$235$	−5.68349	+	3.28136i	−0.370750	+	0.214053i
$236$	−18.0267	−	1.72748i	−1.17344	−	0.112449i
$237$	7.01326	−	5.88482i	0.455560	−	0.382260i
$238$	0.343847	−	0.0438225i	0.0222883	−	0.00284059i
$239$	−10.7517	−	6.20747i	−0.695467	−	0.401528i	0.110190	−	0.993911i	$-0.464854\pi$
$239$	−10.7517	−	6.20747i	−0.695467	−	0.401528i	−0.805657	+	0.592382i	$0.798187\pi$
$240$	−14.9710	−	2.89589i	−0.966372	−	0.186929i
$241$	−3.08075	+	8.46430i	−0.198449	+	0.545234i	−0.998503	−	0.0546939i	$-0.982582\pi$
$241$	−3.08075	+	8.46430i	−0.198449	+	0.545234i	0.800054	+	0.599928i	$0.204804\pi$
$242$	−3.68906	−	3.40858i	−0.237142	−	0.219112i
$243$	2.10658	+	11.9470i	0.135137	+	0.766400i
$244$	−4.72809	−	4.80695i	−0.302685	−	0.307733i
$245$	6.21522	+	5.21519i	0.397076	+	0.333186i
$246$	0.930089	+	0.597954i	0.0593003	+	0.0381241i
$247$	16.2420	−	10.8679i	1.03345	−	0.691507i
$248$	7.58044	+	1.09382i	0.481359	+	0.0694575i
$249$	−4.58775	+	5.46747i	−0.290737	+	0.346487i
$250$	1.45227	−	6.42493i	0.0918498	−	0.406348i
$251$	−9.86546	+	1.73955i	−0.622703	+	0.109799i	−0.476093	−	0.879395i	$-0.657947\pi$
$251$	−9.86546	+	1.73955i	−0.622703	+	0.109799i	−0.146610	+	0.989194i	$0.546836\pi$
$252$	−1.99189	−	7.68759i	−0.125477	−	0.484273i
$253$	−8.05104	−	2.93034i	−0.506165	−	0.184229i
$254$	20.6896	+	0.989063i	1.29818	+	0.0620593i
$255$	0.149230	−	0.258474i	0.00934516	−	0.0161863i
$256$	−11.9098	−	10.6844i	−0.744364	−	0.667774i
$257$	0.755271	+	0.900097i	0.0471125	+	0.0561465i	0.789086	−	0.614283i	$-0.210554\pi$
$257$	0.755271	+	0.900097i	0.0471125	+	0.0561465i	−0.741974	+	0.670429i	$0.766110\pi$
$258$	18.3153	−	9.43829i	1.14026	−	0.587602i
$259$	−16.4113	−	28.4251i	−1.01975	−	1.76625i
$260$	25.8950	−	2.04987i	1.60594	−	0.127127i
$261$	−0.645458	−	0.113812i	−0.0399528	−	0.00704477i
$262$	−10.2141	+	24.3734i	−0.631027	+	1.50579i
$263$	10.0964	+	27.7395i	0.622568	+	1.71049i	0.700612	+	0.713542i	$0.252910\pi$
$263$	10.0964	+	27.7395i	0.622568	+	1.71049i	−0.0780441	+	0.996950i	$0.524868\pi$
$264$	10.5861	−	9.46148i	0.651530	−	0.582314i
$265$			2.73492i			0.168005i
$266$	18.9405	−	3.69897i	1.16132	−	0.226798i
$267$			3.91533i			0.239614i
$268$	−1.12824	+	4.07552i	−0.0689182	+	0.248952i
$269$	3.18316	+	8.74565i	0.194081	+	0.533232i	0.998116	−	0.0613489i	$-0.0195402\pi$
$269$	3.18316	+	8.74565i	0.194081	+	0.533232i	−0.804036	+	0.594581i	$0.797318\pi$
$270$	−21.2231	−	8.89391i	−1.29160	−	0.541266i
$271$	−5.26894	−	0.929056i	−0.320065	−	0.0564361i	0.0113075	−	0.999936i	$-0.496401\pi$
$271$	−5.26894	−	0.929056i	−0.320065	−	0.0564361i	−0.331373	+	0.943500i	$0.607512\pi$
$272$	0.273766	−	0.152078i	0.0165995	−	0.00922106i
$273$	−9.23492	−	15.9953i	−0.558923	−	0.968082i
$274$	10.3782	+	20.1392i	0.626967	+	1.21665i
$275$	−8.31768	−	9.91262i	−0.501575	−	0.597754i
$276$	2.54237	−	5.33646i	0.153033	−	0.321217i
$277$	7.47083	−	12.9398i	0.448878	−	0.777480i	−0.549435	−	0.835537i	$-0.685157\pi$
$277$	7.47083	−	12.9398i	0.448878	−	0.777480i	0.998313	+	0.0580563i	$0.0184903\pi$
$278$	0.792364	−	16.5750i	0.0475228	−	0.994100i
$279$	3.22739	+	1.17468i	0.193219	+	0.0703260i
$280$	24.3666	+	8.01642i	1.45618	+	0.479073i
$281$	19.3541	−	3.41264i	1.15457	−	0.203581i	0.436598	−	0.899657i	$-0.356183\pi$
$281$	19.3541	−	3.41264i	1.15457	−	0.203581i	0.717968	+	0.696076i	$0.245072\pi$
$282$	4.11217	+	0.929502i	0.244876	+	0.0553511i
$283$	−6.74711	+	8.04090i	−0.401074	+	0.477982i	−0.928347	−	0.371714i	$-0.878770\pi$
$283$	−6.74711	+	8.04090i	−0.401074	+	0.477982i	0.527273	+	0.849696i	$0.323215\pi$
$284$	2.40563	+	5.27231i	0.142748	+	0.312854i
$285$	7.33963	−	14.9078i	0.434762	−	0.883062i
$286$	−13.0797	+	20.3449i	−0.773420	+	1.20302i
$287$	−1.42490	−	1.19563i	−0.0841089	−	0.0705758i
$288$	−4.24919	−	5.78133i	−0.250386	−	0.340668i
$289$	−2.95095	−	16.7357i	−0.173586	−	0.984453i
$290$	1.43669	−	1.55491i	0.0843652	−	0.0913076i
$291$	4.25987	−	11.7039i	0.249718	−	0.686094i
$292$	16.9637	−	23.8052i	0.992725	−	1.39309i
$293$	−14.0762	−	8.12692i	−0.822343	−	0.474780i	0.0288809	−	0.999583i	$-0.490806\pi$
$293$	−14.0762	−	8.12692i	−0.822343	−	0.474780i	−0.851224	+	0.524803i	$0.824139\pi$
$294$	−0.658935	−	5.17024i	−0.0384299	−	0.301534i
$295$	20.0939	−	16.8608i	1.16991	−	0.981671i
$296$	−23.3006	−	18.3429i	−1.35432	−	1.06616i
$297$	18.5556	−	10.7131i	1.07671	−	0.621637i
$298$	−17.3457	+	13.1963i	−1.00481	+	0.764439i
$299$	−1.74859	+	9.91672i	−0.101123	+	0.573499i
$300$	7.35523	−	5.06005i	0.424654	−	0.292142i
$301$	−32.5706	+	11.8547i	−1.87734	+	0.683295i
$302$	−10.9033	+	3.38830i	−0.627416	+	0.194975i
$303$	21.1307			1.21393
$304$	14.6492	−	9.45514i	0.840192	−	0.542289i
$305$	9.76629			0.559216
$306$	0.134109	−	0.0416756i	0.00766651	−	0.00238243i
$307$	23.4603	−	8.53887i	1.33895	−	0.487339i	0.429470	−	0.903081i	$-0.358700\pi$
$307$	23.4603	−	8.53887i	1.33895	−	0.487339i	0.909482	+	0.415742i	$0.136478\pi$
$308$	−19.6776	+	13.5372i	−1.12123	+	0.771355i
$309$	−2.60461	+	14.7715i	−0.148171	+	0.840321i
$310$	−8.82909	+	6.71697i	−0.501458	+	0.381498i
$311$	13.2821	−	7.66844i	0.753160	−	0.434837i	−0.0736742	−	0.997282i	$-0.523473\pi$
$311$	13.2821	−	7.66844i	0.753160	−	0.434837i	0.826835	+	0.562445i	$0.190139\pi$
$312$	−13.1117	−	10.3219i	−0.742303	−	0.584362i
$313$	−8.05392	+	6.75804i	−0.455234	+	0.381987i	−0.841374	−	0.540453i	$-0.818253\pi$
$313$	−8.05392	+	6.75804i	−0.455234	+	0.381987i	0.386140	+	0.922440i	$0.373808\pi$
$314$	0.563966	+	4.42508i	0.0318265	+	0.249722i
$315$	9.96181	+	5.75145i	0.561284	+	0.324058i
$316$	−8.07501	+	11.3317i	−0.454255	+	0.637456i
$317$	6.17206	−	16.9576i	0.346657	−	0.952433i	−0.636758	−	0.771064i	$-0.719725\pi$
$317$	6.17206	−	16.9576i	0.346657	−	0.952433i	0.983415	−	0.181369i	$-0.0580529\pi$
$318$	1.19230	−	1.29042i	0.0668611	−	0.0723630i
$319$	0.342295	+	1.94125i	0.0191648	+	0.108689i
$320$	23.1302	−	1.44647i	1.29302	−	0.0808604i
$321$	−9.03087	−	7.57780i	−0.504054	−	0.422952i
$322$	−5.37746	+	8.36439i	−0.299674	+	0.466129i
$323$	0.0813310	+	0.331436i	0.00452538	+	0.0184416i
$324$	2.97732	+	6.52524i	0.165407	+	0.362513i
$325$	−9.77580	+	11.6503i	−0.542264	+	0.646245i
$326$	12.5188	+	2.82970i	0.693350	+	0.156723i
$327$	−20.7982	+	3.66729i	−1.15015	+	0.202802i
$328$	−1.59636	−	0.525189i	−0.0881440	−	0.0289987i
$329$	−6.66440	−	2.42564i	−0.367420	−	0.133730i
$330$	−0.982004	+	20.5419i	−0.0540576	+	1.13080i
$331$	−11.4669	+	19.8613i	−0.630278	+	1.09167i	0.357216	+	0.934022i	$0.383726\pi$
$331$	−11.4669	+	19.8613i	−0.630278	+	1.09167i	−0.987495	+	0.157652i	$0.949607\pi$
$332$	4.66555	−	9.79301i	0.256055	−	0.537461i
$333$	−8.54777	−	10.1868i	−0.468415	−	0.558235i
$334$	7.50557	+	14.5648i	0.410687	+	0.796951i
$335$	−3.06263	−	5.30463i	−0.167329	−	0.289823i
$336$	−8.00207	−	14.4051i	−0.436549	−	0.785864i
$337$	−8.84318	−	1.55929i	−0.481719	−	0.0849400i	−0.0724847	−	0.997370i	$-0.523093\pi$
$337$	−8.84318	−	1.55929i	−0.481719	−	0.0849400i	−0.409234	+	0.912430i	$0.634204\pi$
$338$	9.26153	+	3.88120i	0.503761	+	0.211109i
$339$	3.54017	+	9.72655i	0.192276	+	0.528273i
$340$	−0.121024	+	0.437173i	−0.00656345	+	0.0237090i
$341$		−	10.3295i		−	0.559374i
$342$	7.29690	−	2.80839i	0.394571	−	0.151860i
$343$		−	13.1464i		−	0.709838i
$344$	−23.3487	+	20.8682i	−1.25888	+	1.12514i
$345$	2.92839	+	8.04569i	0.157659	+	0.433166i
$346$	−1.66632	+	3.97626i	−0.0895819	+	0.213765i
$347$	27.4438	+	4.83908i	1.47326	+	0.259775i	0.851881	−	0.523735i	$-0.175462\pi$
$347$	27.4438	+	4.83908i	1.47326	+	0.259775i	0.621378	+	0.783511i	$0.286573\pi$
$348$	−1.35574	+	0.107321i	−0.0726755	+	0.00575304i
$349$	−3.63403	−	6.29433i	−0.194525	−	0.336928i	0.752220	−	0.658913i	$-0.228983\pi$
$349$	−3.63403	−	6.29433i	−0.194525	−	0.336928i	−0.946745	+	0.321985i	$0.895650\pi$
$350$	−13.3500	+	6.87956i	−0.713589	+	0.367728i
$351$	−16.1869	−	19.2908i	−0.863991	−	1.02966i
$352$	−11.9682	+	17.9559i	−0.637905	+	0.957052i
$353$	−5.67899	+	9.83630i	−0.302262	+	0.523533i	−0.976648	−	0.214846i	$-0.931075\pi$
$353$	−5.67899	+	9.83630i	−0.302262	+	0.523533i	0.674386	+	0.738379i	$0.264408\pi$
$354$	−16.8314	−	0.804623i	−0.894579	−	0.0427652i
$355$	−7.88791	−	2.87096i	−0.418647	−	0.152375i
$356$	−1.49257	−	5.76049i	−0.0791059	−	0.305305i
$357$	0.317636	−	0.0560077i	0.0168111	−	0.00296424i
$358$	1.35185	−	5.98064i	0.0714473	−	0.316086i
$359$	10.3569	−	12.3428i	0.546614	−	0.651429i	−0.420043	−	0.907504i	$-0.637985\pi$
$359$	10.3569	−	12.3428i	0.546614	−	0.651429i	0.966657	+	0.256075i	$0.0824294\pi$
$360$	10.2861	+	1.48422i	0.542123	+	0.0782255i
$361$	5.73704	+	18.1132i	0.301949	+	0.953324i
$362$	−2.39118	−	1.53729i	−0.125678	−	0.0807981i
$363$	−3.58019	−	3.00413i	−0.187911	−	0.157676i
$364$	19.6846	+	20.0130i	1.03175	+	1.04896i
$365$	7.35228	+	41.6969i	0.384836	+	2.18251i
$366$	−4.60802	−	4.25766i	−0.240865	−	0.222552i
$367$	9.70967	−	26.6771i	0.506841	−	1.39253i	−0.377638	−	0.925953i	$-0.623264\pi$
$367$	9.70967	−	26.6771i	0.506841	−	1.39253i	0.884479	−	0.466580i	$-0.154514\pi$
$368$	−1.70619	+	8.82053i	−0.0889412	+	0.459802i
$369$	−0.652639	−	0.376801i	−0.0339750	−	0.0196155i
$370$	42.6086	−	5.43038i	2.21512	−	0.282312i
$371$	−2.26407	+	1.89978i	−0.117545	+	0.0986317i
$372$	7.09412	+	0.679821i	0.367813	+	0.0352471i
$373$	0.671383	−	0.387623i	0.0347629	−	0.0200704i	−0.482518	−	0.875886i	$-0.660278\pi$
$373$	0.671383	−	0.387623i	0.0347629	−	0.0200704i	0.517281	+	0.855816i	$0.326944\pi$
$374$	−0.255733	−	0.336147i	−0.0132236	−	0.0173818i
$375$	1.06432	−	6.03607i	0.0549614	−	0.311701i
$376$	−6.40443	+	0.200058i	−0.330283	+	0.0103172i
$377$	2.17704	−	0.792377i	0.112123	−	0.0408095i
$378$	−7.37968	−	23.7473i	−0.379570	−	1.22143i
$379$	−8.20752			−0.421592			−0.210796	−	0.977530i	$-0.567606\pi$
$379$	−8.20752			−0.421592			−0.210796	+	0.977530i	$0.567606\pi$
$380$	−5.11553	+	24.7313i	−0.262421	+	1.26869i
$381$	19.2735			0.987413
$382$	−2.97834	−	9.58410i	−0.152385	−	0.490365i
$383$	−28.3957	+	10.3352i	−1.45095	+	0.528103i	−0.942857	−	0.333198i	$-0.891872\pi$
$383$	−28.3957	+	10.3352i	−1.45095	+	0.528103i	−0.508095	+	0.861301i	$0.669650\pi$
$384$	−11.5441	−	9.40125i	−0.589108	−	0.479756i
$385$	6.00747	−	34.0700i	0.306169	−	1.73637i
$386$	3.11004	+	4.08798i	0.158297	+	0.208073i
$387$	−12.1614	+	7.02139i	−0.618199	+	0.356917i
$388$	−1.80574	+	18.8434i	−0.0916728	+	0.956631i
$389$	7.57457	−	6.35582i	0.384046	−	0.322253i	−0.430242	−	0.902713i	$-0.641572\pi$
$389$	7.57457	−	6.35582i	0.384046	−	0.322253i	0.814288	+	0.580461i	$0.197127\pi$
$390$	23.9766	−	3.05577i	1.21410	−	0.154735i
$391$	−0.152287	−	0.0879228i	−0.00770147	−	0.00444645i
$392$	2.94042	+	7.35560i	0.148514	+	0.371514i
$393$	−8.41035	+	23.1072i	−0.424246	+	1.16561i
$394$	−17.5822	−	16.2454i	−0.885777	−	0.818429i
$395$	−3.49981	−	19.8484i	−0.176095	−	0.998682i
$396$	−6.89881	+	6.78563i	−0.346678	+	0.340991i
$397$	−5.36709	−	4.50352i	−0.269367	−	0.226025i	0.498092	−	0.867124i	$-0.334034\pi$
$397$	−5.36709	−	4.50352i	−0.269367	−	0.226025i	−0.767458	+	0.641099i	$0.778479\pi$
$398$	−7.85494	−	5.04993i	−0.393732	−	0.253130i
$399$	17.4396	−	4.27950i	0.873073	−	0.214243i
$400$	−8.89255	+	10.2486i	−0.444627	+	0.512429i
$401$	12.7238	−	15.1637i	0.635397	−	0.757237i	−0.348238	−	0.937406i	$-0.613220\pi$
$401$	12.7238	−	15.1637i	0.635397	−	0.757237i	0.983636	+	0.180169i	$0.0576644\pi$
$402$	−0.867542	+	3.83805i	−0.0432691	+	0.191425i
$403$	−11.9559	+	2.10814i	−0.595565	+	0.105014i
$404$	−31.0889	+	8.05528i	−1.54673	+	0.400765i
$405$	−9.76242	−	3.55323i	−0.485098	−	0.176561i
$406$	2.28519	+	0.109243i	0.113412	+	0.00542165i
$407$	−19.9972	+	34.6362i	−0.991224	+	1.71685i
$408$	0.247690	−	0.153510i	0.0122625	−	0.00759987i
$409$	11.1288	+	13.2628i	0.550286	+	0.655805i	0.967461	−	0.253021i	$-0.0814243\pi$
$409$	11.1288	+	13.2628i	0.550286	+	0.655805i	−0.417175	+	0.908826i	$0.636980\pi$
$410$	2.16378	−	1.11504i	0.106861	−	0.0550680i
$411$	10.5406	+	18.2569i	0.519931	+	0.900546i
$412$	−1.79898	−	22.7257i	−0.0886295	−	1.11962i
$413$	27.9159	+	4.92233i	1.37365	+	0.242212i
$414$	−1.55711	+	3.71565i	−0.0765276	+	0.182614i
$415$	5.37394	+	14.7648i	0.263796	+	0.724774i
$416$	23.2256	+	10.1879i	1.13873	+	0.499504i
$417$		−	15.4405i		−	0.756126i
$418$	−15.4429	−	17.7335i	−0.755338	−	0.867374i
$419$			7.36000i			0.359560i	0.983707	+	0.179780i	$0.0575385\pi$
$419$			7.36000i			0.359560i	−0.983707	+	0.179780i	$0.942461\pi$
$420$	23.0033	+	6.36809i	1.12245	+	0.310731i
$421$	−1.21485	−	3.33777i	−0.0592081	−	0.162673i	0.906562	−	0.422073i	$-0.138697\pi$
$421$	−1.21485	−	3.33777i	−0.0592081	−	0.162673i	−0.965770	+	0.259400i	$0.916475\pi$
$422$	1.95358	+	0.818679i	0.0950986	+	0.0398527i
$423$	−2.82970	−	0.498952i	−0.137585	−	0.0242599i
$424$	−1.26227	+	2.35307i	−0.0613015	+	0.114275i
$425$	−0.132791	−	0.230001i	−0.00644133	−	0.0111567i
$426$	2.47013	+	4.79338i	0.119678	+	0.232240i
$427$	6.78403	+	8.08490i	0.328302	+	0.391256i
$428$	16.1756	+	7.70629i	0.781875	+	0.372498i
$429$	−11.2528	+	19.4904i	−0.543289	+	0.941005i
$430$	2.16591	−	45.3073i	0.104449	−	2.18491i
$431$	23.3773	+	8.50864i	1.12604	+	0.409847i	0.836855	−	0.547425i	$-0.184392\pi$
$431$	23.3773	+	8.50864i	1.12604	+	0.409847i	0.289190	+	0.957272i	$0.406614\pi$
$432$	−14.1550	−	17.4474i	−0.681034	−	0.839440i
$433$	−2.58798	+	0.456330i	−0.124370	+	0.0219298i	−0.235487	−	0.971878i	$-0.575668\pi$
$433$	−2.58798	+	0.456330i	−0.124370	+	0.0219298i	0.111117	+	0.993807i	$0.464557\pi$
$434$	−11.6936	−	2.64318i	−0.561310	−	0.126877i
$435$	1.26622	−	1.50902i	0.0607106	−	0.0723520i
$436$	29.2017	−	13.3241i	1.39851	−	0.638108i
$437$	−8.78331	−	4.32433i	−0.420163	−	0.206861i
$438$	14.7089	−	22.8791i	0.702820	−	1.09320i
$439$	6.48906	+	5.44497i	0.309706	+	0.259874i	0.784370	−	0.620293i	$-0.212986\pi$
$439$	6.48906	+	5.44497i	0.309706	+	0.259874i	−0.474665	+	0.880167i	$0.657431\pi$
$440$	−6.38602	−	30.5970i	−0.304442	−	1.45865i
$441$	0.616846	+	3.49831i	0.0293736	+	0.166586i
$442$	−0.336881	+	0.364602i	−0.0160238	+	0.0173424i
$443$	5.66756	−	15.5715i	0.269274	−	0.739824i	−0.729184	−	0.684317i	$-0.760100\pi$
$443$	5.66756	−	15.5715i	0.269274	−	0.739824i	0.998458	−	0.0555069i	$-0.0176775\pi$
$444$	−22.4714	−	16.0132i	−1.06645	−	0.759955i
$445$	7.46461	+	4.30970i	0.353856	+	0.204299i
$446$	1.40500	+	11.0242i	0.0665289	+	0.522009i
$447$	−15.5354	+	13.0357i	−0.734799	+	0.616569i
$448$	17.2646	+	18.1433i	0.815674	+	0.857190i
$449$	−20.3983	+	11.7770i	−0.962656	+	0.555790i	−0.896990	−	0.442052i	$-0.854251\pi$
$449$	−20.3983	+	11.7770i	−0.962656	+	0.555790i	−0.0656669	+	0.997842i	$0.520917\pi$
$450$	−4.84256	+	3.68411i	−0.228280	+	0.173671i
$451$	−0.393574	+	2.23207i	−0.0185327	+	0.105104i
$452$	−8.91641	−	12.9608i	−0.419392	−	0.609624i
$453$	−9.98337	+	3.63365i	−0.469060	+	0.170724i
$454$	7.23603	−	2.24866i	0.339604	−	0.105535i
$455$	−40.6604			−1.90619
$456$	13.1954	−	9.43881i	0.617931	−	0.442013i
$457$	−35.6608			−1.66814			−0.834070	−	0.551659i	$-0.813995\pi$
$457$	−35.6608			−1.66814			−0.834070	+	0.551659i	$0.813995\pi$
$458$	−4.24318	+	1.31860i	−0.198271	+	0.0616143i
$459$	0.413234	−	0.150405i	0.0192881	−	0.00702030i
$460$	−7.37556	−	10.7210i	−0.343887	−	0.499870i
$461$	5.18964	−	29.4319i	0.241706	−	1.37078i	−0.586315	−	0.810083i	$-0.699422\pi$
$461$	5.18964	−	29.4319i	0.241706	−	1.37078i	0.828021	−	0.560697i	$-0.189467\pi$
$462$	−17.6875	+	13.4563i	−0.822897	+	0.626042i
$463$	8.24455	−	4.75999i	0.383157	−	0.221216i	−0.296034	−	0.955177i	$-0.595664\pi$
$463$	8.24455	−	4.75999i	0.383157	−	0.221216i	0.679191	+	0.733962i	$0.262331\pi$
$464$	1.95375	−	0.674723i	0.0907004	−	0.0313232i
$465$	−7.90761	+	6.63527i	−0.366706	+	0.307703i
$466$	−2.55370	−	20.0372i	−0.118298	−	0.928207i
$467$	13.8707	+	8.00827i	0.641861	+	0.370579i	0.785331	−	0.619076i	$-0.212493\pi$
$467$	13.8707	+	8.00827i	0.641861	+	0.370579i	−0.143470	+	0.989655i	$0.545826\pi$
$468$	9.26199	+	6.60014i	0.428136	+	0.305092i
$469$	2.26395	−	6.22016i	0.104540	−	0.287220i
$470$	6.29846	−	6.81676i	0.290526	−	0.314434i
$471$	0.720782	+	4.08776i	0.0332119	+	0.188354i
$472$	25.0702	−	5.23250i	1.15395	−	0.240846i
$473$	32.3534	+	27.1478i	1.48761	+	1.24825i
$474$	−7.00170	+	10.8908i	−0.321599	+	0.500232i
$475$	−8.22278	−	12.2889i	−0.377287	−	0.563854i
$476$	−0.445976	+	0.203489i	−0.0204413	+	0.00932688i
$477$	−0.769692	+	0.917283i	−0.0352418	+	0.0419995i
$478$	17.1253	+	3.87097i	0.783295	+	0.177054i
$479$	11.6151	−	2.04805i	0.530706	−	0.0935778i	0.0981272	−	0.995174i	$-0.468715\pi$
$479$	11.6151	−	2.04805i	0.530706	−	0.0935778i	0.432579	+	0.901596i	$0.357604\pi$
$480$	21.4337	−	2.37211i	0.978312	−	0.108272i
$481$	44.1708	+	16.0769i	2.01401	+	0.733041i
$482$	0.608271	−	12.7240i	0.0277060	−	0.579564i
$483$	−4.62635	+	8.01307i	−0.210506	+	0.364608i
$484$	6.41262	+	3.05507i	0.291483	+	0.138867i
$485$	−17.6246	−	21.0042i	−0.800294	−	0.953753i
$486$	−7.85887	−	15.2504i	−0.356486	−	0.691772i
$487$	10.2230	+	17.7067i	0.463247	+	0.802367i	0.999121	−	0.0419308i	$-0.0133509\pi$
$487$	10.2230	+	17.7067i	0.463247	+	0.802367i	−0.535873	+	0.844298i	$0.680018\pi$
$488$	8.40270	+	4.50753i	0.380372	+	0.204046i
$489$	11.7611	+	2.07380i	0.531854	+	0.0937803i
$490$	−10.5824	−	4.43474i	−0.478065	−	0.200341i
$491$	−12.7994	−	35.1661i	−0.577630	−	1.58703i	−0.792163	−	0.610309i	$-0.791045\pi$
$491$	−12.7994	−	35.1661i	−0.577630	−	1.58703i	0.214533	−	0.976717i	$-0.431177\pi$
$492$	−1.50704	−	0.417200i	−0.0679427	−	0.0188088i
$493$			0.0404571i			0.00182210i
$494$	−17.3739	+	21.4936i	−0.781687	+	0.967043i
$495$		−	14.0163i		−	0.629987i
$496$	−10.6965	+	1.70416i	−0.480287	+	0.0765191i
$497$	−3.10255	−	8.52418i	−0.139168	−	0.382362i
$498$	3.90120	−	9.30925i	0.174817	−	0.417158i
$499$	−36.4883	−	6.43387i	−1.63344	−	0.288019i	−0.719689	−	0.694296i	$-0.755716\pi$
$499$	−36.4883	−	6.43387i	−1.63344	−	0.288019i	−0.913750	+	0.406277i	$0.866827\pi$
$500$	0.735117	+	9.28640i	0.0328754	+	0.415300i
$501$	7.62307	+	13.2035i	0.340574	+	0.589891i
$502$	12.5933	−	6.48962i	0.562067	−	0.289646i
$503$	−1.85009	−	2.20485i	−0.0824914	−	0.0983094i	0.723220	−	0.690618i	$-0.242661\pi$
$503$	−1.85009	−	2.20485i	−0.0824914	−	0.0983094i	−0.805711	+	0.592308i	$0.798217\pi$
$504$	5.91639	+	9.54619i	0.263537	+	0.425221i
$505$	23.2591	−	40.2860i	1.03502	−	1.79270i
$506$	12.1028	+	0.578573i	0.538035	+	0.0257207i
$507$	8.78043	+	3.19581i	0.389952	+	0.141931i
$508$	−28.3565	+	7.34729i	−1.25812	+	0.325983i
$509$	−10.1796	+	1.79493i	−0.451201	+	0.0795589i	−0.394631	−	0.918840i	$-0.629128\pi$
$509$	−10.1796	+	1.79493i	−0.451201	+	0.0795589i	−0.0565701	+	0.998399i	$0.518016\pi$
$510$	−0.0930596	+	0.411700i	−0.00412075	+	0.0182304i
$511$	−29.4110	+	35.0507i	−1.30107	+	1.55055i
$512$	20.5683	+	9.43100i	0.909000	+	0.416795i
$513$	22.4032	−	9.87511i	0.989127	−	0.435997i
$514$	−1.39775	−	0.898614i	−0.0616522	−	0.0396362i
$515$	25.2950	+	21.2251i	1.11463	+	0.935288i
$516$	−20.7739	+	20.4331i	−0.914519	+	0.899516i
$517$	1.50063	+	8.51047i	0.0659974	+	0.374290i
$518$	34.0930	+	31.5009i	1.49796	+	1.38407i
$519$	−1.37206	+	3.76971i	−0.0602268	+	0.165472i
$520$	−34.1111	+	13.6360i	−1.49587	+	0.597979i
$521$	−32.7090	−	18.8846i	−1.43301	−	0.827348i	−0.435659	−	0.900112i	$-0.643485\pi$
$521$	−32.7090	−	18.8846i	−1.43301	−	0.827348i	−0.997349	+	0.0727637i	$0.976818\pi$
$522$	0.919460	−	0.117183i	0.0402437	−	0.00512897i
$523$	22.4623	−	18.8481i	0.982206	−	0.824169i	−0.00221480	−	0.999998i	$-0.500705\pi$
$523$	22.4623	−	18.8481i	0.982206	−	0.824169i	0.984421	+	0.175829i	$0.0562605\pi$
$524$	3.56512	−	37.2030i	0.155743	−	1.62522i
$525$	−12.1023	+	6.98726i	−0.528187	+	0.304949i
$526$	−25.2770	−	33.2251i	−1.10213	−	1.44869i
$527$	0.0368142	−	0.208784i	0.00160365	−	0.00909475i
$528$	−10.3258	+	17.2206i	−0.449373	+	0.749429i
$529$	−16.8726	+	6.14113i	−0.733592	+	0.267005i
$530$	−1.14780	−	3.69353i	−0.0498571	−	0.160437i
$531$	11.4845			0.498387
$532$	−24.0269	+	12.9445i	−1.04170	+	0.561214i
$533$	2.66383			0.115383
$534$	−1.64319	−	5.28768i	−0.0711077	−	0.228820i
$535$	−24.3876	+	8.87638i	−1.05437	+	0.383759i
$536$	−0.186723	−	5.97751i	−0.00806519	−	0.258189i
$537$	0.990723	−	5.61867i	0.0427529	−	0.242463i
$538$	−7.96926	−	10.4752i	−0.343579	−	0.451616i
$539$	9.25233	−	5.34183i	0.398526	−	0.230089i
$540$	32.3946	+	3.10433i	1.39404	+	0.133589i
$541$	1.95274	−	1.63855i	0.0839549	−	0.0704466i	−0.599844	−	0.800117i	$-0.704771\pi$
$541$	1.95274	−	1.63855i	0.0839549	−	0.0704466i	0.683799	+	0.729670i	$0.260326\pi$
$542$	7.50564	−	0.956578i	0.322395	−	0.0410885i
$543$	−2.29075	−	1.32256i	−0.0983054	−	0.0567567i
$544$	−0.305899	+	0.320276i	−0.0131153	+	0.0137317i
$545$	−15.9014	+	43.6887i	−0.681141	+	1.87142i
$546$	19.1848	+	17.7261i	0.821032	+	0.758607i
$547$	−0.169432	−	0.960896i	−0.00724439	−	0.0410850i	0.980971	−	0.194153i	$-0.0621958\pi$
$547$	−0.169432	−	0.960896i	−0.00724439	−	0.0410850i	−0.988216	+	0.153068i	$0.951085\pi$
$548$	−22.4678	−	22.8425i	−0.959777	−	0.975785i
$549$	3.27558	+	2.74854i	0.139798	+	0.117305i
$550$	15.3932	+	9.89629i	0.656369	+	0.421979i
$551$	0.148782	+	2.24751i	0.00633832	+	0.0957473i
$552$	−1.19388	+	8.27390i	−0.0508149	+	0.352161i
$553$	14.0001	−	16.6847i	0.595347	−	0.709507i
$554$	−4.65879	+	20.6107i	−0.197933	+	0.875665i
$555$	39.3606	−	6.94034i	1.67077	−	0.294601i
$556$	5.88610	+	22.7171i	0.249626	+	0.963421i
$557$	8.89834	+	3.23873i	0.377035	+	0.137229i	0.523584	−	0.851974i	$-0.324595\pi$
$557$	8.89834	+	3.23873i	0.377035	+	0.137229i	−0.146549	+	0.989203i	$0.546817\pi$
$558$	−4.85161	−	0.231930i	−0.205385	−	0.00981840i
$559$	24.8191	−	42.9880i	1.04974	−	1.81820i
$560$	−36.2716	−	0.600028i	−1.53275	−	0.0253558i
$561$	−0.252623	−	0.301064i	−0.0106657	−	0.0127109i
$562$	−24.7056	+	12.7313i	−1.04214	+	0.537039i
$563$	−15.1232	−	26.1942i	−0.637367	−	1.10395i	−0.986008	−	0.166696i	$-0.946690\pi$
$563$	−15.1232	−	26.1942i	−0.637367	−	1.10395i	0.348641	−	0.937256i	$-0.386643\pi$
$564$	−5.94360	+	0.470499i	−0.250271	+	0.0198116i
$565$	22.4405	+	3.95687i	0.944079	+	0.166467i
$566$	5.73741	−	13.6909i	0.241161	−	0.575472i
$567$	−3.83985	−	10.5499i	−0.161258	−	0.443054i
$568$	−5.46151	−	6.11069i	−0.229160	−	0.256399i
$569$		−	12.8421i		−	0.538369i	−0.963089	−	0.269184i	$-0.913246\pi$
$569$		−	12.8421i		−	0.538369i	0.963089	−	0.269184i	$-0.0867541\pi$
$570$	−3.65570	+	23.2134i	−0.153120	+	0.972302i
$571$			11.1572i			0.466915i	0.972367	+	0.233458i	$0.0750040\pi$
$571$			11.1572i			0.466915i	−0.972367	+	0.233458i	$0.924996\pi$
$572$	9.12588	−	32.9652i	0.381572	−	1.37835i
$573$	−3.19400	−	8.77545i	−0.133431	−	0.366600i
$574$	2.42611	+	1.01670i	0.101264	+	0.0424364i
$575$	7.50312	+	1.32300i	0.312902	+	0.0551730i
$576$	8.16487	+	6.02442i	0.340203	+	0.251017i
$577$	5.34339	+	9.25502i	0.222448	+	0.385291i	0.955551	−	0.294827i	$-0.0952619\pi$
$577$	5.34339	+	9.25502i	0.222448	+	0.385291i	−0.733103	+	0.680118i	$0.761929\pi$
$578$	11.0089	+	21.3632i	0.457911	+	0.888592i
$579$	3.07222	+	3.66132i	0.127677	+	0.152159i
$580$	−1.28769	+	2.70287i	−0.0534684	+	0.112231i
$581$	−8.48989	+	14.7049i	−0.352220	+	0.610063i
$582$	−0.841077	+	17.5940i	−0.0348638	+	0.729293i
$583$	3.38414	+	1.23173i	0.140157	+	0.0510129i
$584$	−12.9190	+	39.2684i	−0.534592	+	1.62494i
$585$	−16.2232	+	2.86059i	−0.670746	+	0.118271i
$586$	22.4208	+	5.06793i	0.926194	+	0.209354i
$587$	9.10535	−	10.8513i	0.375818	−	0.447882i	−0.544672	−	0.838649i	$-0.683346\pi$
$587$	9.10535	−	10.8513i	0.375818	−	0.447882i	0.920490	+	0.390767i	$0.127790\pi$
$588$	3.05975	+	6.70590i	0.126182	+	0.276546i
$589$	1.27733	−	11.7339i	0.0526315	−	0.483488i
$590$	−20.0607	+	31.2036i	−0.825888	+	1.28463i
$591$	−17.0633	−	14.3178i	−0.701889	−	0.588955i
$592$	39.1658	+	14.9934i	1.60971	+	0.616224i
$593$	−1.39125	−	7.89016i	−0.0571317	−	0.324010i	0.942825	−	0.333288i	$-0.108158\pi$
$593$	−1.39125	−	7.89016i	−0.0571317	−	0.324010i	−0.999957	+	0.00927734i	$0.997047\pi$
$594$	−20.5634	+	22.2556i	−0.843727	+	0.913157i
$595$	0.242850	−	0.667224i	0.00995587	−	0.0273535i
$596$	17.8873	−	25.1013i	0.732693	−	1.02819i
$597$	−7.52502	−	4.34457i	−0.307979	−	0.177811i
$598$	−1.80038	−	14.1264i	−0.0736232	−	0.577673i
$599$	−34.0092	+	28.5371i	−1.38958	+	1.16599i	−0.424067	+	0.905631i	$0.639398\pi$
$599$	−34.0092	+	28.5371i	−1.38958	+	1.16599i	−0.965511	+	0.260363i	$0.916158\pi$
$600$	−7.80968	+	9.92048i	−0.318829	+	0.405002i
$601$	−28.8637	+	16.6645i	−1.17737	+	0.679758i	−0.955406	−	0.295296i	$-0.904582\pi$
$601$	−28.8637	+	16.6645i	−1.17737	+	0.679758i	−0.221969	+	0.975054i	$0.571248\pi$
$602$	39.0116	−	29.6791i	1.58999	−	1.20963i
$603$	0.465692	−	2.64107i	0.0189645	−	0.107553i
$604$	13.3030	−	9.15184i	0.541292	−	0.372383i
$605$	−9.66821	+	3.51894i	−0.393069	+	0.143065i
$606$	−28.5372	+	8.86817i	−1.15924	+	0.360245i
$607$	−13.9779			−0.567345			−0.283672	−	0.958921i	$-0.591553\pi$
$607$	−13.9779			−0.567345			−0.283672	+	0.958921i	$0.591553\pi$
$608$	−15.8158	+	18.9172i	−0.641414	+	0.767195i
$609$	2.12879			0.0862628
$610$	−13.1894	+	4.09873i	−0.534025	+	0.165953i
$611$	9.54417	−	3.47379i	0.386116	−	0.140535i
$612$	−0.163625	+	0.112566i	−0.00661415	+	0.00455022i
$613$	−4.97045	+	28.1888i	−0.200755	+	1.13854i	0.703227	+	0.710965i	$0.251742\pi$
$613$	−4.97045	+	28.1888i	−0.200755	+	1.13854i	−0.903982	+	0.427571i	$0.859369\pi$
$614$	−28.0997	+	21.3777i	−1.13401	+	0.862732i
$615$	1.96154	−	1.13250i	0.0790971	−	0.0456667i
$616$	20.8933	−	26.5404i	0.841817	−	1.06934i
$617$	−22.3135	+	18.7233i	−0.898310	+	0.753771i	−0.969859	−	0.243666i	$-0.921650\pi$
$617$	−22.3135	+	18.7233i	−0.898310	+	0.753771i	0.0715497	+	0.997437i	$0.477206\pi$
$618$	−2.68177	−	21.0421i	−0.107877	−	0.846438i
$619$	21.0830	+	12.1723i	0.847396	+	0.489244i	0.859771	−	0.510679i	$-0.170606\pi$
$619$	21.0830	+	12.1723i	0.847396	+	0.489244i	−0.0123753	+	0.999923i	$0.503939\pi$
$620$	9.10475	−	12.7767i	0.365656	−	0.513125i
$621$	−4.31472	+	11.8546i	−0.173144	+	0.475709i
$622$	−14.7193	+	15.9305i	−0.590190	+	0.638756i
$623$	1.61748	+	9.17316i	0.0648028	+	0.367515i
$624$	22.0393	+	8.43705i	0.882279	+	0.337752i
$625$	−23.3291	−	19.5755i	−0.933165	−	0.783018i
$626$	8.04064	−	12.5068i	0.321369	−	0.499874i
$627$	−15.1411	−	15.7960i	−0.604677	−	0.630830i
$628$	−2.61876	−	5.73941i	−0.104500	−	0.229027i
$629$	−0.527633	+	0.628808i	−0.0210381	+	0.0250722i
$630$	−15.8673	−	3.58659i	−0.632167	−	0.142893i
$631$	3.45710	−	0.609581i	0.137625	−	0.0242670i	−0.104411	−	0.994534i	$-0.533296\pi$
$631$	3.45710	−	0.609581i	0.137625	−	0.0242670i	0.242036	+	0.970267i	$0.422185\pi$
$632$	6.14966	−	18.6924i	0.244620	−	0.743545i
$633$	1.85210	+	0.674108i	0.0736142	+	0.0267934i
$634$	−1.21862	+	25.4916i	−0.0483978	+	1.01240i
$635$	21.2148	−	36.7452i	0.841885	−	1.45819i
$636$	−1.06865	+	2.24310i	−0.0423748	+	0.0889449i
$637$	−8.07120	−	9.61888i	−0.319793	−	0.381114i
$638$	−1.27698	−	2.47802i	−0.0505560	−	0.0981056i
$639$	−1.83760	−	3.18281i	−0.0726942	−	0.125910i
$640$	−30.6305	+	11.6608i	−1.21078	+	0.460933i
$641$	−3.21901	−	0.567598i	−0.127143	−	0.0224188i	0.109714	−	0.993963i	$-0.465006\pi$
$641$	−3.21901	−	0.567598i	−0.127143	−	0.0224188i	−0.236858	+	0.971544i	$0.576117\pi$
$642$	15.3765	+	6.44378i	0.606862	+	0.254316i
$643$	12.1157	+	33.2877i	0.477797	+	1.31274i	0.911359	+	0.411613i	$0.135034\pi$
$643$	12.1157	+	33.2877i	0.477797	+	1.31274i	−0.433562	+	0.901124i	$0.642743\pi$
$644$	3.75192	−	13.5530i	0.147846	−	0.534062i
$645$		−	42.2063i		−	1.66187i
$646$	−0.248936	−	0.413474i	−0.00979424	−	0.0162679i
$647$		−	15.0857i		−	0.593078i	−0.955021	−	0.296539i	$-0.904167\pi$
$647$		−	15.0857i		−	0.593078i	0.955021	−	0.296539i	$-0.0958325\pi$
$648$	−6.75941	−	7.56286i	−0.265535	−	0.297097i
$649$	−11.8135	−	32.4573i	−0.463721	−	1.27406i
$650$	8.31285	−	19.8366i	0.326057	−	0.778055i
$651$	−10.9858	−	1.93710i	−0.430569	−	0.0759210i
$652$	−18.0942	+	1.43235i	−0.708625	+	0.0560952i
$653$	0.273124	+	0.473065i	0.0106882	+	0.0185124i	0.871320	−	0.490715i	$-0.163264\pi$
$653$	0.273124	+	0.473065i	0.0106882	+	0.0185124i	−0.860632	+	0.509228i	$0.829931\pi$
$654$	26.5491	−	13.6813i	1.03815	−	0.534982i
$655$	34.7967	+	41.4691i	1.35962	+	1.62033i
$656$	2.37630	+	0.0393103i	0.0927789	+	0.00153481i
$657$	−9.26885	+	16.0541i	−0.361612	+	0.626331i
$658$	10.0183	+	0.478924i	0.390555	+	0.0186704i
$659$	37.6501	+	13.7035i	1.46664	+	0.533813i	0.947186	−	0.320686i	$-0.103913\pi$
$659$	37.6501	+	13.7035i	1.46664	+	0.533813i	0.519453	+	0.854499i	$0.326136\pi$
$660$	−7.29485	−	28.1541i	−0.283952	−	1.09590i
$661$	45.3693	−	7.99983i	1.76466	−	0.311157i	0.805201	−	0.593002i	$-0.202057\pi$
$661$	45.3693	−	7.99983i	1.76466	−	0.311157i	0.959460	+	0.281844i	$0.0909461\pi$
$662$	7.15074	−	31.6352i	0.277921	−	1.22954i
$663$	−0.296908	+	0.353842i	−0.0115310	+	0.0137421i
$664$	−2.19091	+	15.1836i	−0.0850237	+	0.589237i
$665$	11.0373	−	37.9594i	0.428008	−	1.47200i
$666$	15.8190	+	10.1701i	0.612976	+	0.394082i
$667$	−0.889078	−	0.746025i	−0.0344252	−	0.0288862i
$668$	−16.2489	−	16.5199i	−0.628689	−	0.639175i
$669$	1.79568	+	10.1838i	0.0694249	+	0.393728i
$670$	6.36236	+	5.87861i	0.245799	+	0.227111i
$671$	4.39844	−	12.0846i	0.169800	−	0.466522i
$672$	16.8524	+	16.0959i	0.650096	+	0.620912i
$673$	16.3438	+	9.43611i	0.630008	+	0.363735i	0.780755	−	0.624837i	$-0.214835\pi$
$673$	16.3438	+	9.43611i	0.630008	+	0.363735i	−0.150747	+	0.988572i	$0.548168\pi$
$674$	12.5972	−	1.60548i	0.485225	−	0.0618409i
$675$	−14.5956	+	12.2472i	−0.561787	+	0.471395i
$676$	−14.1366	−	1.35469i	−0.543716	−	0.0521037i
$677$	26.5149	−	15.3084i	1.01905	−	0.588349i	0.105222	−	0.994449i	$-0.466445\pi$
$677$	26.5149	−	15.3084i	1.01905	−	0.588349i	0.913829	+	0.406100i	$0.133111\pi$
$678$	−8.86307	−	11.6500i	−0.340384	−	0.447416i
$679$	5.14534	−	29.1807i	0.197460	−	1.11985i
$680$	−0.0200294	−	0.641196i	−0.000768092	−	0.0245888i
$681$	6.62550	−	2.41148i	0.253890	−	0.0924082i
$682$	4.33510	+	13.9501i	0.166000	+	0.534176i
$683$	−47.0432			−1.80006			−0.900029	−	0.435829i	$-0.856455\pi$
$683$	−47.0432			−1.80006			−0.900029	+	0.435829i	$0.856455\pi$
$684$	−8.67588	+	6.85512i	−0.331731	+	0.262112i
$685$	46.4093			1.77321
$686$	5.51729	+	17.7543i	0.210651	+	0.677861i
$687$	−3.88517	+	1.41409i	−0.148228	+	0.0539508i
$688$	22.7746	−	37.9817i	0.868273	−	1.44804i
$689$	0.734994	−	4.16836i	0.0280010	−	0.158802i
$690$	−7.33144	−	9.63677i	−0.279103	−	0.366866i
$691$	0.680964	−	0.393155i	0.0259051	−	0.0149563i	−0.486992	−	0.873407i	$-0.661906\pi$
$691$	0.680964	−	0.393155i	0.0259051	−	0.0149563i	0.512897	+	0.858450i	$0.328572\pi$
$692$	0.581613	−	6.06929i	0.0221096	−	0.230720i
$693$	11.6032	−	9.73627i	0.440771	−	0.369850i
$694$	−39.0939	+	4.98243i	−1.48398	+	0.189130i
$695$	−29.4375	−	16.9958i	−1.11663	−	0.644686i
$696$	1.78590	−	0.713918i	0.0676943	−	0.0270610i
$697$	−0.0159101	+	0.0437126i	−0.000602638	+	0.00165573i
$698$	7.54939	+	6.97540i	0.285749	+	0.264023i
$699$	−3.26378	−	18.5098i	−0.123448	−	0.700106i
$700$	15.1421	−	14.8936i	0.572316	−	0.562927i
$701$	−28.6734	−	24.0598i	−1.08298	−	0.908727i	−0.0868142	−	0.996225i	$-0.527669\pi$
$701$	−28.6734	−	24.0598i	−1.08298	−	0.908727i	−0.996165	+	0.0874973i	$0.972113\pi$
$702$	29.9564	+	19.2590i	1.13063	+	0.726883i
$703$	−26.9991	+	36.8725i	−1.01829	+	1.39067i
$704$	8.62732	−	29.2724i	0.325154	−	1.10324i
$705$	5.55113	−	6.61557i	0.209068	−	0.249157i
$706$	3.54140	−	15.6674i	0.133283	−	0.589649i
$707$	49.5069	−	8.72939i	1.86190	−	0.328303i
$708$	23.0686	−	5.97717i	0.866971	−	0.224636i
$709$	30.0394	+	10.9335i	1.12815	+	0.410615i	0.837622	−	0.546250i	$-0.183945\pi$
$709$	30.0394	+	10.9335i	1.12815	+	0.410615i	0.290533	+	0.956865i	$0.406168\pi$
$710$	11.8576	+	0.566849i	0.445006	+	0.0212735i
$711$	4.41213	−	7.64204i	0.165468	−	0.286599i
$712$	4.43329	+	7.15318i	0.166145	+	0.268077i
$713$	3.90934	+	4.65897i	0.146406	+	0.174480i
$714$	−0.405464	+	0.208944i	−0.0151741	+	0.00781955i
$715$	24.7724	+	42.9071i	0.926436	+	1.60463i
$716$	0.684283	+	8.64423i	0.0255728	+	0.323050i
$717$	16.0889	+	2.83690i	0.600850	+	0.105946i
$718$	−8.80695	+	21.0156i	−0.328673	+	0.784297i
$719$	0.247417	+	0.679772i	0.00922709	+	0.0253512i	0.944221	−	0.329313i	$-0.106817\pi$
$719$	0.247417	+	0.679772i	0.00922709	+	0.0253512i	−0.934994	+	0.354665i	$0.884595\pi$
$720$	−14.5143	+	2.31241i	−0.540916	+	0.0861786i
$721$			35.6839i			1.32894i
$722$	−15.3497	−	22.0542i	−0.571255	−	0.820773i
$723$		−	11.8532i		−	0.440824i
$724$	3.87448	+	1.07258i	0.143994	+	0.0398623i
$725$	−0.599523	−	1.64718i	−0.0222657	−	0.0611746i
$726$	6.09585	+	2.55457i	0.226238	+	0.0948088i
$727$	−13.3127	−	2.34739i	−0.493741	−	0.0870598i	−0.0787667	−	0.996893i	$-0.525098\pi$
$727$	−13.3127	−	2.34739i	−0.493741	−	0.0870598i	−0.414974	+	0.909833i	$0.636209\pi$
$728$	−34.9833	−	18.7664i	−1.29657	−	0.695527i
$729$	−13.3612	−	23.1423i	−0.494859	−	0.857121i
$730$	−27.4287	−	53.2263i	−1.01518	−	1.96999i
$731$	0.557184	+	0.664026i	0.0206082	+	0.0245599i
$732$	8.01003	+	3.81610i	0.296059	+	0.141047i
$733$	−21.2697	+	36.8401i	−0.785613	+	1.36072i	0.143019	+	0.989720i	$0.454319\pi$
$733$	−21.2697	+	36.8401i	−0.785613	+	1.36072i	−0.928632	+	0.371002i	$0.879014\pi$
$734$	−1.91710	+	40.1026i	−0.0707614	+	1.48021i
$735$	−10.0327	−	3.65160i	−0.370061	−	0.134691i
$736$	−1.39759	−	12.6282i	−0.0515158	−	0.465483i
$737$	−7.94317	+	1.40060i	−0.292590	+	0.0515916i
$738$	1.03953	+	0.234972i	0.0382656	+	0.00864945i
$739$	−0.408212	+	0.486488i	−0.0150163	+	0.0178957i	−0.773500	−	0.633796i	$-0.781496\pi$
$739$	−0.408212	+	0.486488i	−0.0150163	+	0.0178957i	0.758484	+	0.651692i	$0.225940\pi$
$740$	−55.2642	+	25.2158i	−2.03155	+	0.926951i
$741$	−15.1929	+	20.7488i	−0.558124	+	0.762227i
$742$	2.26034	−	3.51585i	0.0829797	−	0.129071i
$743$	−29.7921	−	24.9985i	−1.09297	−	0.917107i	−0.0960331	−	0.995378i	$-0.530615\pi$
$743$	−29.7921	−	24.9985i	−1.09297	−	0.917107i	−0.996932	+	0.0782714i	$0.975060\pi$
$744$	−9.86596	+	2.05917i	−0.361704	+	0.0754927i
$745$	7.75259	+	43.9671i	0.284033	+	1.61083i
$746$	−0.744029	+	0.805254i	−0.0272408	+	0.0294824i
$747$	−2.35286	+	6.46444i	−0.0860868	+	0.236522i
$748$	0.486444	+	0.346642i	0.0177861	+	0.0126745i
$749$	−24.2888	−	14.0231i	−0.887492	−	0.512394i
$750$	1.09585	+	8.59843i	0.0400148	+	0.313970i
$751$	−22.5368	+	18.9106i	−0.822380	+	0.690059i	−0.953528	−	0.301304i	$-0.902578\pi$
$751$	−22.5368	+	18.9106i	−0.822380	+	0.690059i	0.131148	+	0.991363i	$0.458134\pi$
$752$	8.56526	−	2.95800i	0.312343	−	0.107867i
$753$	11.4163	−	6.59121i	0.416034	−	0.240197i
$754$	−2.60756	+	1.98377i	−0.0949617	+	0.0722447i
$755$	−4.06135	+	23.0330i	−0.147807	+	0.838258i
$756$	19.9326	+	28.9738i	0.724942	+	1.05377i
$757$	−17.9630	+	6.53799i	−0.652875	+	0.237627i	−0.647157	−	0.762356i	$-0.724042\pi$
$757$	−17.9630	+	6.53799i	−0.652875	+	0.237627i	−0.00571806	+	0.999984i	$0.501820\pi$
$758$	11.0843	−	3.44454i	0.402600	−	0.125111i
$759$	11.2745			0.409237
$760$	−3.47070	−	35.5467i	−0.125896	−	1.28941i
$761$	−6.81878			−0.247181			−0.123590	−	0.992333i	$-0.539441\pi$
$761$	−6.81878			−0.247181			−0.123590	+	0.992333i	$0.539441\pi$
$762$	−26.0290	+	8.08874i	−0.942933	+	0.293024i
$763$	−47.2129	+	17.1841i	−1.70922	+	0.622105i
$764$	8.04453	+	11.6934i	0.291041	+	0.423054i
$765$	0.0499539	−	0.283303i	0.00180609	−	0.0102428i
$766$	34.0111	−	25.8749i	1.22887	−	0.934897i
$767$	−35.1567	+	20.2977i	−1.26943	+	0.732908i
$768$	19.5359	+	7.85160i	0.704942	+	0.283320i
$769$	−27.3710	+	22.9670i	−0.987022	+	0.828210i	−0.985134	−	0.171788i	$-0.945045\pi$
$769$	−27.3710	+	22.9670i	−0.987022	+	0.828210i	−0.00188826	+	0.999998i	$0.500601\pi$
$770$	6.18543	+	48.5330i	0.222907	+	1.74901i
$771$	−1.33904	−	0.773098i	−0.0482245	−	0.0278424i
$772$	−5.91578	−	4.21562i	−0.212914	−	0.151723i
$773$	−3.45061	+	9.48048i	−0.124110	+	0.340989i	−0.986151	−	0.165849i	$-0.946964\pi$
$773$	−3.45061	+	9.48048i	−0.124110	+	0.340989i	0.862041	+	0.506838i	$0.169186\pi$
$774$	13.4773	−	14.5863i	0.484432	−	0.524295i
$775$	1.59505	+	9.04598i	0.0572959	+	0.324941i
$776$	−5.46957	−	26.2060i	−0.196346	−	0.940742i
$777$	33.0868	+	27.7631i	1.18698	+	0.995997i
$778$	−7.56209	+	11.7625i	−0.271114	+	0.421705i
$779$	−0.723098	+	2.48687i	−0.0259077	+	0.0891015i
$780$	−31.0982	+	14.1894i	−1.11349	+	0.508061i
$781$	−7.10495	+	8.46735i	−0.254235	+	0.302986i
$782$	0.242564	+	0.0548284i	0.00867406	+	0.00196066i
$783$	2.85836	−	0.504005i	0.102149	−	0.0180117i
$784$	−7.05807	−	8.69975i	−0.252074	−	0.310705i
$785$	8.58673	+	3.12532i	0.306474	+	0.111547i
$786$	1.66056	−	34.7362i	0.0592301	−	1.23900i
$787$	−4.49406	+	7.78394i	−0.160196	+	0.277468i	−0.934939	−	0.354809i	$-0.884546\pi$
$787$	−4.49406	+	7.78394i	−0.160196	+	0.277468i	0.774743	+	0.632276i	$0.217879\pi$
$788$	30.5627	+	14.5606i	1.08875	+	0.518698i
$789$	−24.9695	−	29.7575i	−0.888937	−	1.05939i
$790$	13.0565	+	25.3366i	0.464530	+	0.901436i
$791$	12.3124	+	21.3257i	0.437778	+	0.758254i
$792$	6.46909	−	12.0593i	0.229869	−	0.428510i
$793$	−14.8850	−	2.62463i	−0.528582	−	0.0932033i
$794$	9.13833	+	3.82957i	0.324307	+	0.135906i
$795$	−1.23091	−	3.38190i	−0.0436559	−	0.119943i
$796$	12.7275	+	3.52340i	0.451114	+	0.124884i
$797$			16.8886i			0.598223i	0.954218	+	0.299112i	$0.0966903\pi$
$797$			16.8886i			0.598223i	−0.954218	+	0.299112i	$0.903310\pi$
$798$	−21.7563	+	13.0986i	−0.770164	+	0.463685i
$799$			0.177365i			0.00627471i
$800$	7.70831	−	17.5728i	0.272530	−	0.621292i
$801$	1.29072	+	3.54623i	0.0456054	+	0.125300i
$802$	−10.8197	+	25.8186i	−0.382057	+	0.911686i
$803$	54.9062	+	9.68144i	1.93760	+	0.341650i
$804$	−0.439136	−	5.54740i	−0.0154871	−	0.195642i
$805$	10.1847	+	17.6404i	0.358962	+	0.621741i
$806$	15.2617	−	7.86472i	0.537572	−	0.277023i
$807$	−7.87233	−	9.38187i	−0.277119	−	0.330258i
$808$	38.6052	−	23.9261i	1.35812	−	0.841719i
$809$	22.3243	−	38.6668i	0.784880	−	1.35945i	−0.144191	−	0.989550i	$-0.546058\pi$
$809$	22.3243	−	38.6668i	0.784880	−	1.35945i	0.929071	−	0.369902i	$-0.120609\pi$
$810$	14.6754	+	0.701557i	0.515642	+	0.0246502i
$811$	−13.4371	−	4.89069i	−0.471839	−	0.171735i	0.0951460	−	0.995463i	$-0.469668\pi$
$811$	−13.4371	−	4.89069i	−0.471839	−	0.171735i	−0.566985	+	0.823728i	$0.691890\pi$
$812$	−3.13201	+	0.811518i	−0.109912	+	0.0284787i
$813$	6.93350	−	1.22256i	0.243168	−	0.0428771i
$814$	12.4702	−	55.1688i	0.437080	−	1.93367i
$815$	16.8994	−	20.1399i	0.591961	−	0.705471i
$816$	−0.270082	+	0.311267i	−0.00945477	+	0.0108965i
$817$	33.3952	+	34.8396i	1.16835	+	1.21888i
$818$	−20.5957	−	13.2410i	−0.720113	−	0.462960i
$819$	−13.6373	−	11.4431i	−0.476527	−	0.399854i
$820$	−2.45423	+	2.41397i	−0.0857055	+	0.0842994i
$821$	6.15480	+	34.9056i	0.214804	+	1.21821i	0.881246	+	0.472657i	$0.156705\pi$
$821$	6.15480	+	34.9056i	0.214804	+	1.21821i	−0.666442	+	0.745557i	$0.732184\pi$
$822$	−21.8973	−	20.2324i	−0.763754	−	0.705684i
$823$	8.58714	−	23.5930i	0.299329	−	0.822400i	−0.695283	−	0.718736i	$-0.744721\pi$
$823$	8.58714	−	23.5930i	0.299329	−	0.822400i	0.994612	−	0.103664i	$-0.0330567\pi$
$824$	11.9671	+	29.9362i	0.416893	+	1.04288i
$825$	14.7467	+	8.51400i	0.513414	+	0.296420i
$826$	−39.7664	+	5.06814i	−1.38365	+	0.176343i
$827$	−1.24282	+	1.04285i	−0.0432171	+	0.0362635i	−0.664140	−	0.747608i	$-0.731202\pi$
$827$	−1.24282	+	1.04285i	−0.0432171	+	0.0362635i	0.620923	+	0.783871i	$0.286758\pi$
$828$	0.543493	−	5.67150i	0.0188877	−	0.197098i
$829$	−0.612854	+	0.353831i	−0.0212853	+	0.0122891i	−0.510605	−	0.859815i	$-0.670578\pi$
$829$	−0.612854	+	0.353831i	−0.0212853	+	0.0122891i	0.489320	+	0.872105i	$0.337245\pi$
$830$	−13.4540	−	17.6846i	−0.466997	−	0.613841i
$831$	−3.41427	+	19.3633i	−0.118440	+	0.671705i
$832$	−35.6420	−	4.01150i	−1.23566	−	0.139074i
$833$	0.206049	−	0.0749958i	0.00713919	−	0.00259845i
$834$	6.48010	+	20.8525i	0.224388	+	0.722064i
$835$	33.5636			1.16152
$836$	28.2982	+	17.4681i	0.978713	+	0.604147i
$837$	−15.2095			−0.525717
$838$	−3.08885	−	9.93973i	−0.106703	−	0.343362i
$839$	34.5798	−	12.5860i	1.19383	−	0.434518i	0.332762	−	0.943011i	$-0.392019\pi$
$839$	34.5798	−	12.5860i	1.19383	−	0.434518i	0.861066	+	0.508493i	$0.169797\pi$
$840$	−33.7387	+	1.05391i	−1.16410	+	0.0363635i
$841$	4.98943	−	28.2965i	0.172049	−	0.975740i
$842$	3.04146	+	3.99783i	0.104816	+	0.137774i
$843$	−22.3965	+	12.9306i	−0.771377	+	0.445354i
$844$	−2.98190	−	0.285752i	−0.102641	−	0.00983599i
$845$	15.7577	−	13.2223i	0.542080	−	0.454860i
$846$	4.03093	−	0.513733i	0.138586	−	0.0176625i
$847$	−9.62901	−	5.55931i	−0.330857	−	0.191020i
$848$	0.717173	−	3.70759i	0.0246278	−	0.127319i
$849$	4.72423	−	12.9797i	0.162135	−	0.445463i
$850$	0.275863	+	0.254888i	0.00946202	+	0.00874260i
$851$	−4.08908	−	23.1903i	−0.140172	−	0.794953i
$852$	−5.34762	−	5.43682i	−0.183207	−	0.186262i
$853$	−37.6785	−	31.6161i	−1.29009	−	1.08251i	−0.991768	−	0.128047i	$-0.959129\pi$
$853$	−37.6785	−	31.6161i	−1.29009	−	1.08251i	−0.298321	−	0.954466i	$-0.596427\pi$
$854$	−12.5550	−	8.07157i	−0.429622	−	0.276204i
$855$	1.73324	−	15.9220i	0.0592754	−	0.544521i
$856$	−25.0794	−	3.61882i	−0.857195	−	0.123689i
$857$	19.1151	−	22.7805i	0.652960	−	0.778167i	−0.333398	−	0.942786i	$-0.608195\pi$
$857$	19.1151	−	22.7805i	0.652960	−	0.778167i	0.986357	+	0.164619i	$0.0526396\pi$
$858$	7.01721	−	31.0445i	0.239563	−	1.05984i
$859$	−1.00555	+	0.177305i	−0.0343088	+	0.00604957i	−0.190776	−	0.981634i	$-0.561100\pi$
$859$	−1.00555	+	0.177305i	−0.0343088	+	0.00604957i	0.156467	+	0.987683i	$0.449989\pi$
$860$	16.0895	+	62.0968i	0.548649	+	2.11748i
$861$	2.30009	+	0.837163i	0.0783867	+	0.0285304i
$862$	−35.1421	−	1.67996i	−1.19694	−	0.0572198i
$863$	−18.1997	+	31.5228i	−0.619524	+	1.07305i	0.370048	+	0.929013i	$0.379341\pi$
$863$	−18.1997	+	31.5228i	−0.619524	+	1.07305i	−0.989573	+	0.144035i	$0.953992\pi$
$864$	26.4388	+	17.6223i	0.899466	+	0.599522i
$865$	5.67673	+	6.76526i	0.193015	+	0.230026i
$866$	3.30357	−	1.70240i	0.112260	−	0.0578500i
$867$	11.1813	+	19.3665i	0.379736	+	0.657722i
$868$	16.9015	−	1.33794i	0.573676	−	0.0454125i
$869$	−26.1363	−	4.60853i	−0.886612	−	0.156334i
$870$	−1.07673	+	2.56935i	−0.0365046	+	0.0871092i
$871$	3.24223	+	8.90797i	0.109859	+	0.301835i
$872$	−33.8453	+	30.2497i	−1.14615	+	1.02438i
$873$		−	12.0049i		−	0.406303i
$874$	13.6768	+	2.15385i	0.462623	+	0.0728550i
$875$		−	14.5815i		−	0.492945i
$876$	−10.2626	+	37.0714i	−0.346741	+	1.25253i
$877$	−14.8862	−	40.8995i	−0.502671	−	1.38108i	−0.888657	−	0.458573i	$-0.848361\pi$
$877$	−14.8862	−	40.8995i	−0.502671	−	1.38108i	0.385986	−	0.922505i	$-0.373861\pi$
$878$	−11.0487	−	4.63013i	−0.372874	−	0.156259i
$879$	21.0638	+	3.71412i	0.710464	+	0.125274i
$880$	21.4653	+	38.6413i	0.723597	+	1.30260i
$881$	−26.6388	−	46.1398i	−0.897486	−	1.55449i	−0.830698	−	0.556723i	$-0.812058\pi$
$881$	−26.6388	−	46.1398i	−0.897486	−	1.55449i	−0.0667877	−	0.997767i	$-0.521275\pi$
$882$	−2.30123	−	4.46561i	−0.0774864	−	0.150365i
$883$	−9.30915	−	11.0942i	−0.313278	−	0.373350i	0.586312	−	0.810085i	$-0.300579\pi$
$883$	−9.30915	−	11.0942i	−0.313278	−	0.373350i	−0.899590	+	0.436735i	$0.856135\pi$
$884$	0.301943	−	0.633780i	0.0101554	−	0.0213163i
$885$	−17.2587	+	29.8930i	−0.580145	+	1.00484i
$886$	−1.11902	+	23.4080i	−0.0375941	+	0.786406i
$887$	−37.1590	−	13.5248i	−1.24768	−	0.454117i	−0.368061	−	0.929802i	$-0.619978\pi$
$887$	−37.1590	−	13.5248i	−1.24768	−	0.454117i	−0.879616	+	0.475684i	$0.842201\pi$
$888$	37.0682	+	12.1952i	1.24393	+	0.409243i
$889$	45.1557	−	7.96216i	1.51447	−	0.267042i
$890$	−11.8897	−	2.68752i	−0.398544	−	0.0900857i
$891$	−8.79340	+	10.4796i	−0.294590	+	0.351079i
$892$	−6.52410	−	14.2985i	−0.218443	−	0.478751i
$893$	0.652262	+	9.85313i	0.0218271	+	0.329722i
$894$	15.5098	−	24.1248i	0.518725	−	0.806853i
$895$	−9.62154	−	8.07343i	−0.321612	−	0.269865i
$896$	−30.9303	−	17.2570i	−1.03331	−	0.576516i
$897$	−2.30100	−	13.0496i	−0.0768280	−	0.435713i
$898$	22.6055	−	24.4657i	0.754355	−	0.816430i
$899$	0.478576	−	1.31488i	0.0159614	−	0.0438536i
$900$	4.99376	−	7.00775i	0.166459	−	0.233592i
$901$	0.0640116	+	0.0369571i	0.00213254	+	0.00123122i
$902$	−0.405233	−	3.17960i	−0.0134928	−	0.105869i
$903$	34.9400	−	29.3181i	1.16273	−	0.975646i
$904$	17.4811	+	13.7616i	0.581411	+	0.457703i
$905$	−5.04296	+	2.91156i	−0.167634	+	0.0967834i
$906$	11.9576	−	9.09710i	0.397266	−	0.302231i
$907$	8.61295	−	48.8464i	0.285988	−	1.62192i	−0.415746	−	0.909481i	$-0.636480\pi$
$907$	8.61295	−	48.8464i	0.285988	−	1.62192i	0.701734	−	0.712439i	$-0.252409\pi$
$908$	−8.82858	+	6.07365i	−0.292987	+	0.201561i
$909$	19.1387	−	6.96593i	0.634792	−	0.231045i
$910$	54.9121	−	17.0644i	1.82032	−	0.565679i
$911$	40.7226			1.34920			0.674599	−	0.738184i	$-0.264316\pi$
$911$	40.7226			1.34920			0.674599	+	0.738184i	$0.264316\pi$
$912$	−13.8592	+	18.2850i	−0.458923	+	0.605478i
$913$	20.6899			0.684736
$914$	48.1601	−	14.9661i	1.59299	−	0.495036i
$915$	−12.0766	+	4.39552i	−0.399240	+	0.145311i
$916$	5.17705	−	3.56157i	0.171055	−	0.117678i
$917$	−10.1586	+	57.6120i	−0.335465	+	1.90252i
$918$	−0.494953	+	0.376549i	−0.0163359	+	0.0124280i
$919$	23.6930	−	13.6792i	0.781562	−	0.451235i	−0.0554219	−	0.998463i	$-0.517650\pi$
$919$	23.6930	−	13.6792i	0.781562	−	0.451235i	0.836983	+	0.547228i	$0.184317\pi$
$920$	14.4601	+	11.3834i	0.476737	+	0.375300i
$921$	−25.1670	+	21.1176i	−0.829281	+	0.695849i
$922$	5.34337	+	41.9260i	0.175975	+	1.38076i
$923$	11.2506	+	6.49552i	0.370317	+	0.213803i
$924$	18.2398	−	25.5959i	0.600044	−	0.842042i
$925$	12.1640	−	33.4202i	0.399948	−	1.09885i
$926$	−9.13664	+	9.88849i	−0.300249	+	0.324956i
$927$	2.51048	+	14.2376i	0.0824548	+	0.467625i
$928$	−2.35538	+	1.73117i	−0.0773191	+	0.0568284i
$929$	20.6304	+	17.3109i	0.676860	+	0.567953i	0.915087	−	0.403256i	$-0.132122\pi$
$929$	20.6304	+	17.3109i	0.676860	+	0.567953i	−0.238227	+	0.971210i	$0.576566\pi$
$930$	7.89458	−	12.2796i	0.258873	−	0.402666i
$931$	11.1708	−	4.92399i	0.366110	−	0.161377i
$932$	11.8580	+	25.9887i	0.388423	+	0.851288i
$933$	−12.9728	+	15.4604i	−0.424710	+	0.506150i
$934$	−22.0934	−	4.99394i	−0.722920	−	0.163407i
$935$	−0.852049	+	0.150239i	−0.0278650	+	0.00491335i
$936$	−15.2783	−	5.02645i	−0.499388	−	0.164295i
$937$	−39.4921	−	14.3740i	−1.29015	−	0.469577i	−0.396375	−	0.918089i	$-0.629732\pi$
$937$	−39.4921	−	14.3740i	−1.29015	−	0.469577i	−0.893777	+	0.448512i	$0.851954\pi$
$938$	−0.447000	+	9.35050i	−0.0145951	+	0.305305i
$939$	6.91755	−	11.9815i	0.225746	−	0.391003i
$940$	−5.64525	+	11.8494i	−0.184128	+	0.386486i
$941$	−19.5593	−	23.3099i	−0.637615	−	0.759880i	0.346377	−	0.938095i	$-0.387412\pi$
$941$	−19.5593	−	23.3099i	−0.637615	−	0.759880i	−0.983991	+	0.178216i	$0.942967\pi$
$942$	−2.68898	−	5.21805i	−0.0876116	−	0.170013i
$943$	−0.667240	−	1.15569i	−0.0217283	−	0.0376345i
$944$	−31.6615	+	17.5880i	−1.03049	+	0.572441i
$945$	−50.1657	−	8.84557i	−1.63189	−	0.287747i
$946$	−55.0869	−	23.0851i	−1.79103	−	0.750561i
$947$	−5.70257	−	15.6677i	−0.185309	−	0.509132i	0.811900	−	0.583797i	$-0.198433\pi$
$947$	−5.70257	−	15.6677i	−0.185309	−	0.509132i	−0.997209	+	0.0746651i	$0.976211\pi$
$948$	4.88517	−	17.6466i	0.158663	−	0.573135i
$949$		−	65.5269i		−	2.12709i
$950$	16.2623	+	13.1453i	0.527620	+	0.426490i
$951$			23.7469i			0.770047i
$952$	0.516893	−	0.461980i	0.0167526	−	0.0149729i
$953$	15.6863	+	43.0977i	0.508129	+	1.39607i	0.883165	+	0.469062i	$0.155408\pi$
$953$	15.6863	+	43.0977i	0.508129	+	1.39607i	−0.375036	+	0.927010i	$0.622370\pi$
$954$	0.654508	−	1.56182i	0.0211905	−	0.0505659i
$955$	−20.2462	−	3.56995i	−0.655152	−	0.115521i
$956$	−24.7525	+	1.95942i	−0.800552	+	0.0633722i
$957$	−1.29697	−	2.24641i	−0.0419250	−	0.0726163i
$958$	−14.8267	+	7.64053i	−0.479029	+	0.246854i
$959$	32.2376	+	38.4193i	1.04101	+	1.24062i
$960$	−27.9509	+	12.1989i	−0.902111	+	0.393718i
$961$	11.8338	−	20.4967i	0.381735	−	0.661184i
$962$	−66.4001	−	3.17425i	−2.14082	−	0.102342i
$963$	−10.6776	−	3.88633i	−0.344081	−	0.125235i
$964$	4.51856	+	17.4392i	0.145533	+	0.561678i
$965$	10.3620	−	1.82710i	0.333565	−	0.0588165i
$966$	2.88498	−	12.7633i	0.0928227	−	0.410653i
$967$	11.9162	−	14.2012i	0.383200	−	0.456680i	−0.539621	−	0.841908i	$-0.681433\pi$
$967$	11.9162	−	14.2012i	0.383200	−	0.456680i	0.922822	+	0.385228i	$0.125877\pi$
$968$	−9.94244	−	1.43464i	−0.319562	−	0.0461111i
$969$	−0.249740	−	0.373236i	−0.00802282	−	0.0119901i
$970$	32.6173	+	20.9696i	1.04728	+	0.673294i
$971$	−40.2577	−	33.7803i	−1.29193	−	1.08406i	−0.991479	−	0.130264i	$-0.958418\pi$
$971$	−40.2577	−	33.7803i	−1.29193	−	1.08406i	−0.300453	−	0.953797i	$-0.597138\pi$
$972$	17.0138	+	17.2975i	0.545717	+	0.554819i
$973$	−6.37869	−	36.1754i	−0.204492	−	1.15973i
$974$	−21.2374	−	19.6226i	−0.680489	−	0.628750i
$975$	6.84488	−	18.8061i	0.219212	−	0.602279i
$976$	−13.2396	−	2.56099i	−0.423790	−	0.0819753i
$977$	42.9769	+	24.8127i	1.37495	+	0.793830i	0.991547	−	0.129749i	$-0.0414173\pi$
$977$	42.9769	+	24.8127i	1.37495	+	0.793830i	0.383407	+	0.923579i	$0.374751\pi$
$978$	−16.7537	+	2.13523i	−0.535726	+	0.0682771i
$979$	8.69457	−	7.29561i	0.277880	−	0.233169i
$980$	16.1528	+	1.54790i	0.515982	+	0.0494459i
$981$	−17.6286	+	10.1779i	−0.562839	+	0.324955i
$982$	32.0443	+	42.1204i	1.02257	+	1.34412i
$983$	−2.09570	+	11.8853i	−0.0668425	+	0.379083i	0.932974	+	0.359943i	$0.117204\pi$
$983$	−2.09570	+	11.8853i	−0.0668425	+	0.379083i	−0.999817	+	0.0191398i	$0.993907\pi$
$984$	2.21036	−	0.0690462i	0.0704637	−	0.00220111i
$985$	−46.0789	+	16.7714i	−1.46820	+	0.534380i
$986$	−0.0169791	−	0.0546376i	−0.000540725	−	0.00174002i
$987$	9.33264			0.297061
$988$	14.4431	−	36.3187i	0.459495	−	1.15545i
$989$	−24.8669			−0.790723
$990$	5.88239	+	18.9291i	0.186955	+	0.601608i
$991$	8.02497	−	2.92085i	0.254922	−	0.0927839i	−0.211398	−	0.977400i	$-0.567802\pi$
$991$	8.02497	−	2.92085i	0.254922	−	0.0927839i	0.466320	+	0.884616i	$0.345580\pi$
$992$	13.7305	−	6.79060i	0.435943	−	0.215602i
$993$	5.24054	−	29.7206i	0.166303	−	0.943153i
$994$	7.76745	+	10.2099i	0.246368	+	0.323838i
$995$	−16.5659	+	9.56435i	−0.525175	+	0.303210i
$996$	−1.36168	+	14.2095i	−0.0431463	+	0.450244i
$997$	36.1681	−	30.3486i	1.14545	−	0.961150i	0.145851	−	0.989307i	$-0.453408\pi$
$997$	36.1681	−	30.3486i	1.14545	−	0.961150i	0.999604	+	0.0281561i	$0.00896354\pi$
$998$	51.9778	−	6.62446i	1.64533	−	0.209694i
$999$	50.9993	+	29.4445i	1.61355	+	0.931582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.3.1	✓	48
3.2	odd	2		684.2.cf.a.307.8		48
4.3	odd	2	inner	76.2.k.a.3.4	yes	48
12.11	even	2		684.2.cf.a.307.5		48
19.13	odd	18	inner	76.2.k.a.51.4	yes	48
57.32	even	18		684.2.cf.a.127.5		48
76.51	even	18	inner	76.2.k.a.51.1	yes	48
228.203	odd	18		684.2.cf.a.127.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.1	✓	48	1.1	even	1	trivial
76.2.k.a.3.4	yes	48	4.3	odd	2	inner
76.2.k.a.51.1	yes	48	76.51	even	18	inner
76.2.k.a.51.4	yes	48	19.13	odd	18	inner
684.2.cf.a.127.5		48	57.32	even	18
684.2.cf.a.127.8		48	228.203	odd	18
684.2.cf.a.307.5		48	12.11	even	2
684.2.cf.a.307.8		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35051 + 0.419681i) q^{2} +(-1.23656 + 0.450071i) q^{3} +(1.64774 - 1.13356i) q^{4} +(-0.503046 + 2.85292i) q^{5} +(1.48110 - 1.12678i) q^{6} +(-2.71118 + 1.56530i) q^{7} +(-1.74954 + 2.22241i) q^{8} +(-0.971618 + 0.815285i) q^{9} +O(q^{10})\)	\(q+(-1.35051 + 0.419681i) q^{2} +(-1.23656 + 0.450071i) q^{3} +(1.64774 - 1.13356i) q^{4} +(-0.503046 + 2.85292i) q^{5} +(1.48110 - 1.12678i) q^{6} +(-2.71118 + 1.56530i) q^{7} +(-1.74954 + 2.22241i) q^{8} +(-0.971618 + 0.815285i) q^{9} +(-0.517948 - 4.06400i) q^{10} +(3.30359 + 1.90733i) q^{11} +(-1.52734 + 2.14332i) q^{12} +(1.53341 - 4.21300i) q^{13} +(3.00454 - 3.25178i) q^{14} +(-0.661968 - 3.75421i) q^{15} +(1.43006 - 3.73563i) q^{16} +(0.0599755 + 0.0503255i) q^{17} +(0.970017 - 1.50882i) q^{18} +(3.51689 + 2.57517i) q^{19} +(2.40508 + 5.27109i) q^{20} +(2.64804 - 3.15581i) q^{21} +(-5.26199 - 1.18940i) q^{22} +(-2.21189 + 0.390015i) q^{23} +(1.16317 - 3.53556i) q^{24} +(-3.18761 - 1.16020i) q^{25} +(-0.302759 + 6.33322i) q^{26} +(2.80841 - 4.86430i) q^{27} +(-2.69294 + 5.65251i) q^{28} +(0.332156 + 0.395848i) q^{29} +(2.46956 + 4.79226i) q^{30} +(-1.35392 - 2.34507i) q^{31} +(-0.363540 + 5.64516i) q^{32} +(-4.94351 - 0.871675i) q^{33} +(-0.102118 - 0.0427943i) q^{34} +(-3.10183 - 8.52220i) q^{35} +(-0.676793 + 2.44476i) q^{36} +10.4844i q^{37} +(-5.83033 - 2.00181i) q^{38} +5.89976i q^{39} +(-5.46025 - 6.10927i) q^{40} +(0.203213 + 0.558324i) q^{41} +(-2.25176 + 5.37328i) q^{42} +(10.9034 + 1.92257i) q^{43} +(7.60552 - 0.602057i) q^{44} +(-1.83717 - 3.18207i) q^{45} +(2.82348 - 1.45500i) q^{46} +(1.45618 + 1.73541i) q^{47} +(-0.0870632 + 5.26296i) q^{48} +(1.40035 - 2.42547i) q^{49} +(4.79180 + 0.229071i) q^{50} +(-0.0968133 - 0.0352372i) q^{51} +(-2.24906 - 8.68012i) q^{52} +(0.929735 - 0.163937i) q^{53} +(-1.75132 + 7.74791i) q^{54} +(-7.10330 + 8.46538i) q^{55} +(1.26459 - 8.76392i) q^{56} +(-5.50785 - 1.60150i) q^{57} +(-0.614709 - 0.395196i) q^{58} +(-6.93627 - 5.82022i) q^{59} +(-5.34638 - 5.43556i) q^{60} +(-0.585413 - 3.32004i) q^{61} +(2.81266 + 2.59881i) q^{62} +(1.35807 - 3.73126i) q^{63} +(-1.87820 - 7.77640i) q^{64} +(11.2480 + 6.49401i) q^{65} +(7.04207 - 0.897497i) q^{66} +(-1.61972 + 1.35911i) q^{67} +(0.155871 + 0.0149369i) q^{68} +(2.55959 - 1.47778i) q^{69} +(7.76564 + 10.2075i) q^{70} +(-0.503163 + 2.85358i) q^{71} +(-0.112009 - 3.58571i) q^{72} +(13.7341 - 4.99880i) q^{73} +(-4.40011 - 14.1593i) q^{74} +4.46384 q^{75} +(8.71402 + 0.256572i) q^{76} -11.9422 q^{77} +(-2.47602 - 7.96767i) q^{78} +(-6.53766 + 2.37952i) q^{79} +(9.93804 + 5.95905i) q^{80} +(-0.622736 + 3.53171i) q^{81} +(-0.508759 - 0.668736i) q^{82} +(4.69715 - 2.71190i) q^{83} +(0.785956 - 8.20167i) q^{84} +(-0.173745 + 0.145789i) q^{85} +(-15.5320 + 1.97952i) q^{86} +(-0.588891 - 0.339996i) q^{87} +(-10.0186 + 4.00497i) q^{88} +(1.01763 - 2.79592i) q^{89} +(3.81656 + 3.52638i) q^{90} +(2.43727 + 13.8225i) q^{91} +(-3.20249 + 3.14996i) q^{92} +(2.72965 + 2.29045i) q^{93} +(-2.69489 - 1.73255i) q^{94} +(-9.11589 + 8.73797i) q^{95} +(-2.09118 - 7.14419i) q^{96} +(-6.08391 + 7.25052i) q^{97} +(-0.873252 + 3.86331i) q^{98} +(-4.76484 + 0.840170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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